The only Baofeng to buy is the UV-B5, do not buy a UV-5R or derivative. The -B5 is actually a somewhat decent radio.
Do not buy a multimode "all in one" for a VHF/UHF FM radio. If you want an all-in-one, the FT991 is the one to buy. VHF SSB is a reasonable, if overlooked, option for the communications needs you describe and is the real application for the "all in one".
An HF radio plus a separate VHF/UHF FM radio gives you a lot more flexibility and is much easier on the user cycle. Using an "all in one" for basic VHF/UHF FM operation is a PITA, plus prevents you from having simultaneous HF operation.
Yes HF communications on the low bands can work on the distances you describe. You really want to find any possible alternative to that however. The only people who suggest using HF for family emergency communications are people who haven't tried it. Just because something is technically possible does not mean it will work reliably, conveniently, or pleasantly. HF operation is orders of magnitude more complex than VHF/UHF FM operation.
As far as mobile/base FM radios, part of your calculus needs to be what the actual frequency needs are in your area, and your desired usage. Some dual band radios, like the TM-V71A, can simultaneously monitor two frequencies at the same time. Some of those can even monitor two frequencies on the same band at the same time. Others can only monitor one frequency at a time regardless of which band it's in.
On your mobile antenna, you mention a spring base. What will be best will depend on whether the vehicle encounters low hanging branches or other obstructions, or whether you are just dealing with rough conditions, vibration etc. Either way I would strongly recommend that you look to the Land Mobile Radio market for antennas (from companies like Maxrad/PC Tel, Larsen, or even Tram/Browning) versus the Amateur radio specific market antennas (from companies like Comet, Diamond, Opek, Jetstream). Amateur marketed antennas tend to be very stiff, so as to stand rigid against airflow while driving. This results in optimum signal pattern from the antenna, as the expense of fragility. The LMR type antennas use much more flexible whips so that the antennas can flex, and have optional springs. Keep in mind that LMR antennas are generally described/specified by their tunable frequencies, not their coverage. As an example a Larsen 5/8 wave for VHF that is advertised for 144-174MHz WILL NOT cover that entire range, you cut the whip to tune it where you want it within that range.
On the FT-8900, it really depends on what frequency bands you genuinely use. I am a big proponent of "alternative" amateur band usage, but also try to be realistic especially with those new to the amateur world. You do need a General class license to operate on 10m FM, and usage tends to be quite limited as there is only one simplex frequency and a handful of repeater pairs. 10m repeaters tend to be used for fun to exploit E skip openings, more than local communications. 6m FM also tends to be very limited with repeaters very few and far between, and limited simplex operation. That might be good if you want privacy, but bad if you want to actually talk to anyone else. 6m does have a little bit of a following for simplex operation in the backcountry, so if it's active in your neck of the woods that might be something to consider.
LMR type 5/8 wave antennas for VHF High Band, when cut for 2m will generally resonate somewhere in the 6m band, so will function as a 6m/2m dual band, if that is of interest. Whatever you do, avoid the specialty 10m/6m/2m/70cm giant antennas marketed for amateur use, those will not hold up to rough off-road service.
You may think you want a setup to move between your vehicle and your house but you don't. Get both. Just plan on it.