In the late 80's and 90's, Ashtabula cranks and then steel rims faded away in adult bike store bikes, replaced by cotterless cranks and aluminum rims. Meanwhile, department store bikes got worse, at least at the low end. Mountain bikes became fashionable. This led to much wider tires and rims, not suitable for the sidepull caliper brakes that were still used. To compound the problem, the calipers got cheaper and flimsier becoming stamped steel rather than cast aluminum. Other parts had many of the same problems--The gauge of metal used in bearings got thinner and weaker, more plastic in inappropriate places, and general cost cutting. Some of these bikes are still sold.
Lately, however the better department store bikes have been improving drastically. Pacific Cycle has been largely responsible for this trend. While bike snobs will (correctly) complain that the Schwinn and Mongoose bikes that they now sell at Walmart aren't as good as before the brands were bought by Pacific, it is also true that they are considerably better than the best you used to find outside a specialty shop. You can get aluminum rims and cantilever or direct pull brakes, both making braking a lot better, especially in the rain, especially with fat tires. Shifting is usually 21 speed index, and far more aluminum parts are used.
In a previous post, I talked about the first bike I bought myself in the 70's, a basic 10 speed as cheap as I could find. I just bought a low-end adult bike as a gift (because I couldn't find a decent used bike in time) and it cost less, and had better features than that mid 70's 10 speed.
If you are close to average men's or woman's size, you can get a fairly decent bike at a mass market store. It will not be assembled as well as a bike from a specialty shop, but most of that is easily corrected with basic tools and a bit of knowledge. These aren't suitable for off-road or high-performance use, but will do fine for basic transportation and recreation within their limits. The biggest problem is fit--If you are the size of an average woman, you will be stuck with a woman's style frame--an engineering compromise resulting in a heavier, weaker frame to allow riding with a dress. If you are a large man, you won't find a bike big enough. If you don't match the stock sizes, you will have to compromise significantly.
A modern bike with hand brakes should have aluminum rims. There used to be well-made steel rims, some with patterned sides to give better rain performance. Since the 1980s, steel rims are just cheap. Aluminum is stronger, lighter and brakes better especially in the rain.
Brakes should be cantilever or direct-pull except for the thinnest road tires. There are now very few department store bikes with wheels and tires narrow enough for side pull brakes.
An adult bike used for more than riding on flat ground should have gears. It is better if it is index (clicks into gear), although that is nearly universal on new bikes now.
Ashtabula cranks are still used. They are much heavier, but work fine. I'm enough of a snob to insist on cotterless for my bikes, but I've also got several bikes already. More important is the right crank length. 170mm is standard, and is unfortunately used even on cheaper bikes meant for smaller people, where a 160 or 165mm would be more appropriate.
Most people would do better with far less tread if their riding is limited to pavement . Because of the long oval contact patch and relatively low speeds, even on wet pavement bicycle tire tread is unnecessary and adds rolling resistance--tread is necessary with a car's rectangular contact patch, wider width and higher speeds. Putting slick or semi-slick tires on a mountain bike with knobby tires is likely the best bang for the buck upgrade. Be cautious of sizes--a 26x1.75 tire is not the same as a 26x1-3/4. You can usually replace a tire with a wider or narrower version, as long as the replacement is the same (decimal or fraction) as the original.
The more aluminum parts, the better. Frame materials are largely irrelevant. Most mid-grade frames are now aluminum, but steel is still used at both ends of the price scale. Slant-parallelogram derailers are better than straight, (although this example is of an older top of the line derailer) but not by a huge amount. A derailer mounted to the frame rather than held on by a claw is better. Quick release wheels are nice, especially front.
Adult bikes typically come in road (what most people would consier a racing bike, the traditional "ten speed" type) mountain and Hybrid. Hybrids are the most useful for most people-more comfortable than a road bike, but easier to pedal than a mountain bike.
Suspension in a department store bike is almost entirely for looks, increases weight, adds reliability problems, and does not improve performance. It is unfortunate that bike makers will often add suspension before they go to aluminum wheels--I wound up buying from Target rather than Walmart because of this.
What did I wind up buying? A Magna from Target. 15 speeds, aluminum rims with bolt-on hubs, a quick-release seat, an almost nothing else. Paint had problems--I found the one with the least scrapes. The rear derailer had the limit screw adjusted wrong so it woudn't shift right into low gear, and the front derailer was crooked. Only took a few minutes to re-adjust if you know what to look for, but it is stuff you wouldn't have to deal with on a bike store bike.
Later: The Magna has some other issues--A shifter screw came loose, the rear bearing cone came loose, and the freewheel snapped a couple teeth. The freewheel was possibly abuse, the rest is poor quality. Don't know that I'd recommend one, but I don't know what in the price range would be better
If you want a road bike there are fantastic bargains available at garage sales and thrift stores, generally priced less than a newer but lower-quality department store bike. I mean a bike that was originally $500+, still in good condition for $25 or less.