I watch a program called Border Security; there is a US, Canadian, Australian and New Zealand version. The common mistake US residents make is to bring their hunting rifles and shotguns on visits to Canada or in transit to Alaska. This is simply not allowed.
At the slightest sign of suspicion, cars are thoroughly searched. I once crossed the Thousnd Island Bridge from New York to Ontario. We were a couple of simple business types driving a Chrysler. Just behind us was a Jaguar Vandenplas driven by a guy in a guru suit, The customs literally were stating to take his car apart, probably a result of a tipoff or surveillance.
Although guns are not confiscated (hand guns are), the owners are asked to send them back home or send them in bond to the destination, subject to import controls.
Asians coming in from overseas often bring along unpackaged food given by their relatives. This is always confiscated. Going to Europe I am always surprised how few questions I’m asked about what I am bringing in.
As @jtsanders points out, bringing in any raw food, unpackaged, can bring bugs and other pests across any border.
Enough room to sleep in very much depends on your height. If you’re short there are various mid-sized crossovers you might fit in. If you’re my height, nothing smaller than a large crossover or minivan will do. I think you need to decide how far off into the wilds you will venture. In all of the West there are places you can’t get to without a full-on off-road vehicle. But most of the typical tourist destinations and campgrounds are easily reachable with any ordinary car. If you need to get to high mountain trailheads or the like or to obscure desert ghost towns, you need more, but those are not places anybody should be going alone.
Your price is going to limit you to older vehicles, but you’ll find something. If I were looking for an older minivan I’d stick with the Toyota Sienna. The Honda Odyssey is similarly nice, but is legendary for developing transmission problems as it ages. The common Chrysler and Dodge models are dogs. There are a few other uncommon models that might be OK (like the Nissan Quest or Mazda MPV), but you aren’t likely to run into one. I have nothing much to say about an SUV because I don’t know which will fit you.
Google diaprepes if you want to know why they might confiscate citrus fruit. When I am in the states, I live in McAllen, the center of a major citrus area.
Honda Odyssey minivan is pretty comfortable for sleeping if the back seats are out, but it doesn’t get as good of gas mileage as a small car, obviously. Around 28 mpg, highway.