It looks like I can only get an auto large enough for my family if I
pick up at the airport.
That’s what I figured.
Ok a van makes sense for your group but please do your homework on driving in Italy (ZTLs, speed cameras, parking). All drivers will need an IDP- required by law. Parking that van will be an issue.
Can you tell us more?- it will help us help you.
When is this trip? Where are you headed after Venice and beyond?
It’s good you are starting in Venice- perfect place to get over jet lag.
Any chance you can add a night to Venice? As it is you have just one full day.
Apartments make sense for a group of your size but keep in mind check in for apartments is usually later afternoon so you have to store your bags (you don’t want to be lugging all that around all day!) If budget allows you might consider hotels rooms for this short stay.
There are several ways to get to the airport- vaporetto ride or walk from your lodging location to P. Roma- then bus to airport is the least expensive (but multiply x6!)
There are also the alilaguna boats and then most expensive is private water taxi (about 150 euros total) so add up the costs of other modes and see the difference.
There are many threads here that explain all these options- here is one.
https://community.ricksteves.com/travel-forum/italy/getting-to-venice-from-airport
A single vaporetto ticket is 9.50 euros now so you might want vaporetto length of stay passes if you plan to ride more than a few times- the pass is a huge money saver and is a true 24 hour pass. You must validate each and every time you board. Fines are high and they do check!
You can stay almost anywhere that fits your needs.Venice is very compact and obviously completely walkable.
I would start my research on booking.com- use the filters for budget, location, #beds, amenities, AC, elevator, bkft) You can book there or find the actual website. Read the reviews there as those reviews can only be left by folks who have actually stayed at the property.
I wouldn’t really want to be near P Roma or the train station but others are OK with those locations.
Use Google maps to pinpoint locations and see how many bridges and canals you would have to cross with luggage to get to that hotel/apartment- the fewer the better.
Do some searches here on the forum for Venice apartments, hotels. Filter by Type:Travel Forum and Date: 1 yr, 6 m etc.
Row Venice gets good reviews here- your family might enjoy
https://rowvenice.org/