I haul bikes frequently enough (before covid, anyhow) to justify getting a dedicated bike-hauling vehicle that also serves as a camper.
They all have pluses and minuses and not everyone will have the same factors in play.
I towed bikes on an open trailer behind a VW diesel for, uh, decades. It works. Normally I wouldn't unload the trailer unless I actually needed to work on the bike - just stick the trailer in the garage with the bike on it. Advantage: Only insuring one vehicle, and it can be one that you like driving, as long as it has enough tow capacity. Disadvantage: you need a secure place to put the trailer and the bike. If you want a trailer that gives protection from the weather (enclosed), you need a bigger tow vehicle.
Pickup truck ... I did this way back in the beginning, but my truck was a 2 wheel drive Toyota. The bad thing nowadays is that the cargo floor heights have gotten insane. No bueno. Most people who show up at the racetrack with a pickup truck ... have the bike in a trailer. YES you can do it, but it's a royal pain. Also, if you want a bed that is long enough then you get a compact cab with iffy rear seat room (whether that matters to you or not, is a question for you to answer yourself), and if you want crew cab long box, it's longer than a normal parking spot ...
The compact cargo vans are a great choice. Front wheel drive, so lower cargo floor, easier loading and unloading. But, check both the height of the back door opening and the length from the seats to the back doors. The original-style Transit Connect needed the front wheel of a bike to be slipped in between the seats of the van, it was just a little bit too short. The new-style Transit Connect is a little longer but I think it's a little lower ... get out a tape measure and do some measurements. I know someone at SOAR who used one as a race-bike hauler ... it's doable. Haven't checked measurements of a ProMaster City. Chrysler minivans have been used, too - the only minor nuisance is that the back door opening isn't quite high enough in many cases but it depends on the bike. The old Chevrolet Astro worked well for this but good luck finding one nowadays that still has rocker panels - and they're awful in other ways.
I ended up with a full-size Ram ProMaster van but the second-smallest configuration - medium wheelbase low roof. With the bike out, even in low roof configuration, I can still stand up inside with my head ducked - so it is also my change-room at the track. I built a raised platform at the front of the cargo area crossways - sleeping quarters, and on the way to/from the track, it's space for clothing and leathers and whatever else. Generator, tires, toolbox, grill go under the platform. Because I will never even come close to approaching the full load capacity, I took a leaf out of the rear springs to lower the rear slightly, so the load floor is even lower. It's very easy to get bikes in and out of.
Aside from being a little wide for parking lots, you *could* daily-drive this. It's shorter than an extended-cab pickup. It almost-barely-not-quite fits in the length of a normal parking spot - the longer configurations would not. I can still tow a trailer with it, and have done so a few times.
For the original poster - perhaps check out a Transit Connect or a ProMaster City.
