If possible I use public transport (trains here in Tokyo), However, if I am traveling with just one care attendant that puts a lot of extra work on them, so if I need to take extra luggage I’ll use a wheelchair taxi/Uber.
I’m not sure about the US, but I’ve found that most hotels don’t have accessible airport pick-up service… but some do, so it is always worth asking. Even if they don’t, having people request it will maybe encourage them to invest in accessible transportation.
This isn’t my first time out, I’m just interested in know how other people manage. My wife and I are headed south in 3 wks and we booked the limo for this one, the last time we took the limo I had a wheelchair everything went fine. Park sleep and fly , the shuttle wasn’t overly comfortable, I’m leary about that route again, maybe next time a different hotel. The limo seems to be the most comfortable option, have another trip for Sept. we decide that one further on.