Here’s your issues which you will need to worry about:
1.) Buying an “off-brand” make/model (i.e. one that’s not presently popular with collectors) will make parts sourcing difficult, if not impossible, with some cars.
2.) Brakes. Forget the issue about older brakes not working as well asmodern ones, that’s minor. The real issue is that they’re single cylinder, rather than dual cylinder like on a modern car. You have a wheel cylinder or a brake line go out on you, and you’ll have nothing to stop with. Nothing. The “emergency brake,” is, in fact, called a “Parking Brake” and in an “Oh shit!” situation will probably fail, or be less than effective in stopping the car in the desired distance.
3.) No seatbelts. It was fairly common for people to have the steering wheel shatter on them in a crash and wind up getting speared by the steering column (if they didn’t go through the windshield first).
4.) Points, condensor, and carbs. These can be hard and/or expensive to get, and generally not too many 20 year old mechanics know how to work on them.
5.) Vacuum “powered” wipers. Depending upon the demands being placed on the engine, you may or may not have functioning wipers. Odds are when you need them, you won’t.
However, there are solutions to these problems. For the “off brand” cars, you will have to do your research, but many of your mechanical parts can be sourced from other vehicles. You can’t expect the clerk at the store to know that the starter used on a DeSoto is the same as on a Plymouth. Join a car club for that make. Talk to the guys in the club, they’ll know what parts interchange, where you can find them, and where you can find parts for those that don’t. (Start with Hemmings Motor News and Google. They’re your friends.)
There are conversion kits to add a dual master cylinder to your car (some of them will even give you power brakes). While purists might scream at what you’re doing, screw it. With the car being a daily driver, its not going to be a pristine trailer queen, and as such will not retain its value like an all points winner at Pebble Beach. It will, however, do more to turn heads and spark interest in old cars than their baby which is only seen at car shows. If you want to get fancy, you can put completely modern brakes (discs or drums) on your car, but this is pricey and can involve completely swapping out things like the front suspension or rear axle.
You can also add seatbelts to the car. Again, the purists will scream, and the mount points might not hold as well as those on a modern car, but its better than nothing.
Points and condensors can all be replaced with a modern aftermarket kit to give you an electronic set up. Some of them simply drop into your existing distributor, and others will require a full swap. Purists will scream, but screw 'em. While they’re digging through the dusty shelves of an abandoned looking parts store for some leftover stock, or scouring the intarwebs for parts, you can be driving your car. Some carbs can be retrofitted with a throttle body system, so you won’t even have to spend time looking for carb parts. (Or making replacement carb gaskets by hand.) Purists probably won’t even know you’ve done it if you don’t take off the air cleaner.
The vacuum motor wipers can be replaced by electric motors fairly easily. Some cars even have retrofit units which bolt up using existing hardware and give you things like variable speed control, while looking completely stock.
As for modern “creature comforts” its all a question of what you want and how much you’re willing pay. There’s lots of mounting set ups so that you can install a modern radio and speakers in such a way that they’re not easy to see (or steal) and you won’t have to perform major surgery to install the units. You want AC? Vintage Air make kits which will fit (and look good) in near every make and model. The same is true of things like power windows, locks, and even remote starting (the last one can be a little tricky depending upon your car, same is true with cruise control). Anti-lock brakes and airbags? Unless you’re made of money, you can forget about those, but everything else is out there.
Another thing you’ll need to know about is if the car has a 6V or 12V electrical system. If its got a 6V system, you’ll want to switch to a 12V setup. You can buy rewound generators that’ll put out 12V. You’ll need a different voltage regulator, starter (you can get a rewound one), bulbs, and you’ll need to either put resistors (someone makes a dedicated kit for this, so you don’t have to spend all day down at Radio Shack trying to figure out which ones will work and how to wire them up) on your gauges or replace them with 12V gauges. (My advice? Get the resistors.)