The main factors that will influence your bike choice are:
your budget
your size, how tall you are, what size bike you need.
Your riding style, how hilly your area is, how far you need to ride, how hard you want to pedal.
Someone that is riding 2 miles, on flat terrain, mostly in the dry does not need as fancy a bike as someone that rides 10 miles, with hills, to get to work or school, raining or not.
Some road bikes are race bikes. That only take very skinny tires and have hard, fast gearing.
Some road bikes are touring bikes or cyclocross bikes, that take fatter tires and fenders, have wider range gearing, and fit racks to carry stuff.
Under a $100, your options are limited. Your best bet is to find a 1980's japanese touring bike or road bike. Univega, Bridgestone, Nishiki, Miyata, Centurion, Shogun, Fuji are good brands to look for. These are higher end 10 speed brands, and realistically go for $200 most of the time, but sometimes you can find deals on CL. Trek made good american bikes, and Raleigh good british bikes. I hesitate to recommend french road bikes, like Motobecane or Peugeot, or most Schwinn 10 speeds, but that is another topic.
Here's a good example of a $100 japanese 10 speed.
This is a 58cm, Nishiki Royale. Pretty sure it's a 1981. This would fit someone 5'10"-6'0" pretty well. This was a $330 bike in 1981. Not super high end, but good quality bike. It has a cromoly frame, made in Japan. Though the tubes are not particularly light, and it does have a high tensile steel fork. Ideally, you'd want to get a bike with cromoly steel fork, but at $100, you can't be too picky.
It has 27" wheels, which take up to 1 1/4" tires. Current road bikes have 700c wheels. :/ The bigger, 27" wheels are a bit heavier, than smaller 700c, but roll over bumps easier, and fit fatter tires and fenders more easily than a lot of 700c bikes.
It has a 10 speed drive train, 2 gears in front, 5 in the back. The gearing is pretty hard and fast. Not really any super low, easy hill climbing gears.
The 27" wheels have aluminum alloy rims, made by araya. They are singlewall, but better quality than what is available new in 27"
The tires do look old and dryrotted. The best thing you can do to any inexpensive $100-300 bike, new or used, is replace the tires, with high quality, flat resistant tires. Being late to work or school because of flats gets old. Sitting on the side of the road fixing flat in the rain, when you just want to be home, is not fun. Spending $20-40 a tire on good rubber is worth it in the long run.
The schwalbe HS129, $16, is the best affordable choice.
http://www.schwalbetires.com/bike_tires/road_tires/hs159
Better tire for $30 each, is the Panaracer Pasela PT. It has kevlar belt for flat protection, and is much lighter, 390g, vs 550g for the cheaper schalbe. It also has nicer tire casing, that has a more supple ride. Pasela is a faster, better riding tire, and has good flat protection. Would be my choice.
http://www.niagaracycle.com/categories/pana-pasela-pt-tire-27x1-1-4-steel-bead
The gears on the bike are 2X5, for 10 speeds. 52X40 in the front, 14-28 in the back. This bike does have suntour bar end shifters, which are pretty cool. You don't have to take your hands off the bars to shift. You do have to be "in the drops" to shift though.
Same shifters on a different bike. These are pretty awesome shifters, IMO, super reliable, have very nice feel, and they sell for quite a bit on Ebay.
Most ten speeds from this era are going to have downtube shifters or stem shifters.
Downtube shifters:
Higher end bikes usually came with downtube shifters. Bar end shifters were more rare, and usually came on more touring type bikes.
Stem shifters:
These are actually way more convenient to use than down tube shifters, you can reach them from the tops of the bars, but at this time, they were seen as for beginners, and that serious bike riders could take their hands off the bars. So most bikes with stem shifters, are lower end, beginner bikes from this era. With heavy, soft frames, and cheap parts, and should be avoided.
It should be noted, that stem shifters are very inexpensive, and is pretty much the cheapest way to convert an old ten speed with downtube shifters, to get the shifters up to your bars.
The 2X5 gearing on bikes this old, is not very wide. 52X14 is your top gear. 40X28 is low gear. Modern bikes with triple rings or compact cranks will have 34X32 low gear, maybe 4 or 5 gears lower than old 10-speed.
Also, old bikes like this, have old fashioned chains and cog tooth profiles. Shimano came out with HG technology chains and cogs with cutaways, that make shifting way smoother, and chains quieter and smoother, in the late 80's.
One of the best things you can do for an old 10-speed is replace the chain and freewheel. $8 for KMC chain, $15 for shimano freewheel. $25 to make your bike shift way smoother, and better under load, and increase your gear range is pretty good.
If the distance between the smallest cog, and the dropout, the distance between the two red lines, in greater than 13mm, 1/2" or so, you have enough room to put a 7 speed freewheel on. 5 speed freewheel is usually about 25mm wide, 7 speed is 32mm. Plus about 5mm for clearance for the chain and dropout.
I am going to show you a crappier 10 speed, for comparison to the nicer quality bike, so you know what to avoid, and what to look for.
This is a cheaper bike. It has cottered, steel cranks, heavier, and more prone to coming loose and creaking than aluminum cranks. Steel rims, heavier, and much worse braking than alloy rims, And lower quality hi-ten frame and fork. The stem shifters and brake levers with "suicide levers" are also indicator of low quality of the bike.
Poor quality steel cottered cranks:
One other weird thing about french bikes in general, motobecane, peugeot, is they have french threaded bottom bracket shells. The tube in the frame the crank spindle/axle goes thru. Most current bikes, and all japanese and english bikes, have english threaded BB shells. And parts are readily available, starting at $12. French bikes, there is one option, and it costs $60, and you have to special order it. Some french bikes have oddball freewheel and headset/stem sizes as well. French bikes are much more likely to cause you issues with parts availability and expensive parts than other bikes.
Better quality aluminum cranks on the Nishiki. These are not super high end, decent quality bike:
This is what cheaper, heavier, steel rims look like, notice the shiny chrome finish:
vs. ligher, better alloy rims. Softer gray, brushed finish.
You can also see higher quality fork lugs, frame lugs, and paint of the midrange Nishiki:
vs. the cheaper in it's day motobecane:
Another give away of a lower quality bike, is stem shifters and suicide levers:
Getting back to the Nishiki.
So you've got your $100 japanese 10-speed, and have put $30-60 worth of good tires into it. It's pretty fast and smooth riding, but the brakes don't work that great, and the shifting is kinda clunky and loud, and doesn't have very low hill climbing gears.
The brake levers on this bike, don't have rubber hoods, have exposed cables, and not that good leverage. Modern brake levers would be a big upgrade, both in braking power, and ride comfort.
$23 Tektros work. Shimanos are $30, or you could look around for used nicer ones.
The brake calipers on the $100 Nishiki, are aluminum, single pivot, Diacompe 500's, A decent quality brake in 1981.
However, modern, shimano dual pivot brakes are much stronger, and easier to adjust, and cost $15 per side, hardly more than the $8-10 new brake pads cost. The main thing you need to make sure you get right, when ordering new brakes, is the caliper reach, that is, the distance between center of bolt the mounts the brake, and center of the brake pad where it hits the rim. There are 3 differnet sizes, short, medium, long.
Pretty sure this nishiki needs short, 39-49mm reach brakes, like this $15 Shimano Soras.
http://www.nashbar.com/bikes/Product_10053_10052_583012_-1___204965
To me, having brakes you can depend on for ~$50 is worth it. Plus more comfy hoods, where you spend most of your time riding.
The best old 10 speed brakes are the type like this mafac racers. Weinman and Diacompe also made similar brakes. These are quite strong, and new brake pads will have them working about the same as new dual pivots.
Lastly, is the gears. The old fashioned teeth on freewheel and old style chain, make a racket, and shift poorly. Just putting a $8 KMC Z50 chain on will make a big difference.
Putting a $13 shimano freewheel on, with HG shift cut outs, makes shifting WAAAAY smoother.
This is the gear ratio chart for the stock 52/40 X 14-28 gearing. 7.5% top gear. 2.9% low gear.
This what the gear ratio chart for a current road bike, with 50/34 compact crank, and 11 speed 11-32 gearing looks like. There are 3 easier gears, going to down to 2.1% low gear. And 3 harder fast gears, going up to 9.2% And the jumps between gears is smaller.
You can add gear range to the old 10-speed, pretty inexpensively.