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Do you need a luggage rack to utilize a car-top luggage carrier, or can you just slap it up on the roof (and secure it, of course)?
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About how much does it cost to retrofit a compact car with a trailer hitch?
TIA
I can answer #2. It depends.
I bought the trailer hitch setup for my 2005 Subaru Baja, and installed it in about an hour in my driveway. It was about $250, but the car was pre-wired for an easy trailer hitch installation.
U-Haul wanted nearly $400 for the whole thing, hitch, wiring, and installation. Depending on the complexity required to wire the electrical connection, it could add a little to this.
You won’t be able to pull a whole lot with a compact car. My car can pull about 1500lbs, but I don’t come anywhere close to that. This would be a small pop-up trailer, or couple of motorcycles on a utility trailer. I currently pull a 14’ aluminum boat on a light trailer, with a small engine, which doesn’t weigh more than a few hundred pounds.
The easiest thing to do is to call a few places nearby, including checking with the dealer for any package they sell… you may not have them install it, but it gives a baseline on pricing for parts.
trailer hitches should be secured to something substantial which the rear of compact cars don’t have. a compact car will not have the power nor drive train to tow a trailer.
does your owners manual say it is suitable for towing?
Just do what this guy did.
Turn green and make a face? 
I wonder how far they got like that.
The Curt Mfg. website lets you put in your car’s year, make, model and spits out which of their hitch models will work. Some cars have frames with pre-drilled holes and spotwelded nuts so all you have to do is bolt on the hitch. It’s an easy DIY project. But if not, you’ll probably have to have it welded on or have holes drilled. I’ve seen smaller cars with hitches…you just need to know the limitations of your vehicle. I’d check the manual and see if it has a section on towing. Of course you might also be interested in one or more of the many other uses for the receiver other than towing, like to attach a bike rack. My Curt hitch cost about $140 but that didn’t include the wiring. I installed it myself if about 40 minutes.
Can’t help on the luggage rack/cartop carrier thing.
My parents used to have a car-top luggage carrier, the kind that looks like a large Rubbermaid tub. They didn’t have a luggage rack; the thing attached to the edges of the windows, I think. Maybe bungee cords were involved somehow. But anyway, no luggage rack required.
I don’t plan to pull much, just a PWC and trailer. And maybe a roll-behind luggage trailer.
A luggage rack is not necessary, though it might make things a bit easier.
I have a car-top carrier from ~25 years ago, looks like this. It has two straps on each side that are meant to grab onto the rain gutters (here’s a photo of a bracket that hooks to a rain gutter). Most cars now don’t have rain gutters. The straps could be hooked into the window opening or into the door opening. However, if they weren’t designed for that, it’s possible the hooks could scratch the paint.
I would expect that modern carriers have hooks designed for door openings and/or window openings.
Check out Thule and Yakima for the car-top carriers - they’ve made it simple, if expensive, to get just the right bits and bobs to securely mount racks and bins. Part of what makes them expensive is the modular design - the base collection of hardware will accept a bicycle carrier in the summer and a ski rack in the winter, for example.
What’s the make/model of the car? As mentioned upthread, this information is widely available, and likely in your owner’s manual as well. Once we have that info, we can give better answers.
I’d disagree, and say that with proper installation, any car could have a hitch installed safely. It may (will) have a lower tow weight rating, and tongue weight limits, but I’d see no impedement in any car that I’ve climbed under in the past 20 years in the US.
The OP states he’s not looking for a great capacity, probably well under 1000lb, which probably isn’t far away from the maximum load of the vehicle’s interior. 4 good size men, and their luggage weighs somewhere in that range.
He may also have restrictions on the routes he can take, crossing the Rocky Mountains may be right out, but the OP is in IL, which isn’t on my radar as being a particularly steep part of the US. Braking capacity probably isn’t an issue with light loads, and the given terrain.
2007 Toyota Yaris.
The manufacturer in the link SmellMyWort provided indicated that they can work with the Yaris, so I’m in the clear.
We picked up many of those when our area had “get rid of all the crap in your basement/garage” day, perfect condition, usually just needed new straps. When we finally tracked down the straps (Sears, IIRC) I was amazed by the variety of replacement clips. There was a clip that would at least work, if not be the perfect shape, for any given roof/door frame.
We also ended up with ~6 of these, fold-up, hitch receiver mounted, cargo carriers.
CMC fnord!