Sorry to hear of your problems with QRM around your home QTH - a couple of quick questions on that point - is your antenna at home vertical or horizontally polarised? Vertical antennas do pick up more noise especially if close to buildings. On the horizontal front, the skyloop (full wave horizontal loop) is one of the best antennas I have found for filtering out local electrical noise, but it needs a lot of space and should not run over the roof of or near to the building where the noise is. An off centre fed dipole is also better than a vertical if that is all you can fit in. Not sure about end-feds, whether they are better or worse for noise reception. Another option might be a magnetic loop if you can locate this so it’s easy to tune and turn. These can be expensive if they have remote tuning though. One more option (again if you have space) is to put up two antennas and use a phasing unit to null out the noise. One antenna picks up mainly noise and the other everything, when phased together you are closer to getting the weaker signals without the noise.
I would also say that any of the latest rigs from the big three have very good digital noise reduction, my favorite, if you can get it in your price range would be the ICOM IC7300. There may be some of those on the second hand market as several upgraded to the IC7610 when it came out.
OK - on to your original question - by going static-mobile you immedaitely lower your noise floor drastically. So the question might be more one of practicalities. While an IC-7300 would be a very nice choice the FT-857D or FT-891 are good rigs and somewhat smaller. They do rely on multi-level menus to save on front panel real-estate but this is probably going to be a one-time set-up in the deeper menus and then leave them alone. The Yaesu FT-450D and the Kenwood TS-590SG are certainly also worth considering.
If you’re thinking of running the digital modes from your parked car then a rig with a USB interface avoids having to have the extra complexity of adapter boxes in between rig and laptop/tablet.
Are you looking specifically for a brand-new rig or lets say less than 1 year old “nearly new” rig or will a second hand, older rig be acceptable?
You have probably more choice at the moment than ever before even in the sub US$1000 range.
For installation in a car, I would recommend sticking with the big-3 rather than the smaller firms. Even if their SDR riigs may be more sensitive, this is less of a problem when you are out in the countryside. The major 3 manufacturer’s rigs seem more sturdy to me as a general rule (there are exceptions I am sure and with the addition of protective panels for example an Elecraft K3S would be a killer rig - but out of your price range).
As much of a question as the rig, is what antenna are you going to use. The simplest and fastest set-up would be a loaded vertical mounted to the car on either a magnetic mount or a boot-lip or similar mount but in comparison if you are able to set up a fibreglass pole with an inverted-V linked dipole (such as the SOTAbeams band hopper or build one yourself) or an OCF (such as the Aerial-51 UL-404 or several other companies - or again build one yourself) it will far, far outperform the loaded whip on the car.
Even though you have a ready 12V supply in the car, as you’re going to be running up to 100 watts when the engine is not running, I’d plan to have a large LifePO 4S battery to power the rig, that is then charged via the correct charger when you are driving and not operating. Otherwise you run the risk of a flat battery when you want to set off to go home and with the modern computer controlled cars that we have nowadays that can turn into a major problem.
Perhaps you should look for a rig that can be used at home when needed or in the car in a static mobile set-up, for that I’d recommend the IC7300 as I feel it would excel in both environments. Rember though in both environments the antenna can make all the difference.