Hi folks, was hoping to get some advice on an upcoming road trip I'm making with my Dad and sister.

Background - We are from the UK and flying into New York JFK late on Fri 23 March 2018. We're then staying nearby somewhere overnight, then early on Sat 24 March flying from La Guardia to Cincinnati OH. Our plan is to then pick up a rental car at Cincinnati Airport, and drop it off somewhere in Seattle WA 12 days later on Thurs 5 Apr. We'll then be staying overnight in Seattle before getting an Amtrak up the coast to Vancouver, where we will again stay overnight, before flying home from Vancouver to the UK on Sat 7 April.

We have established stops for the start and end of the trip, but currently the middle is fairly flexible:

Fri 23 Mar - fly to New York
Sat 24 Mar - fly to Cincinnati OH then pick up car and drive to Louisville KY
Sun 25 Mar - drive to Nashville TN
Mon 26 Mar - drive to Memphis TN
Tue 27 Mar - drive to St Louis MO
...
...
...
Wed 4 Apr - drive to Portland OR
Thurs 5 Apr - drive to Seattle WA (drop off car)
Fri 6 Apr - Amtrak to Vancouver
Sat 7 Apr - fly back to UK

So basically we have 8 days of driving from Wed 28 Mar to Wed 4 Apr to get from St Louis MO to Portland OR. I'm not worried about the pace, it will be fairly rapid but I've done two cross-country trips before so know what to expect.

However, what I am unsure about is what sort of car would be best for a trip like this. The previous road trips I've done have been in the height of summer, whereas this time it will be spring. Our route between St Louis and Portland hasn't been set in stone but we're very keen to drive through the northern states of Mississippi, N Dakota, Wyoming, Montana etc - as I understand it, in late March/early April the weather in these states can get extremely cold/snowy/icy. Normally I would just opt for a small-ish compact car but not sure if that would be sufficient for a route like this at that time of year? Would something bigger like a 4WD SUV be more appropriate? Do we need to worry about snow tyres and chains etc? (Sorry I am a bit naive with this, we don't get much snow here in England)

Also one other thing, we were hoping to skirt the northern edge of Yellowstone - however, having done some research it seems that a lot of the park is closed for a couple of weeks in late March/early April to clear all the snow away. Apart from, it seems, one road which remains open year round (from Gardiner MT to Cooke City MT) - would anyone know if it is worth taking this road? I know we don't have enough time to properly see Yellowstone but even just driving through the northern edge (or possibly staying the night if there are any accommodations open at that time of year) would be awesome.

Anyway, thank you for taking the time to read, any and all advice on any of the above would be much appreciated. Thank you!!!