I have used various types of bike racks and mounts and I like the hitch mounted ones, and specifically the ones with a "tray" that the bike wheels rest on top of, instead of those that comes up high and the top tube of the frame rest onto.
The one I have now, I just leave it on without removing it. It has two trays for two bikes - I don't remember the brand but I got it for like $120 via eBay many years ago. It swings down and out of the way when not in use, and I can still swing my rear open without having to remove the rack. When I want to mount a bike, I swing it up to horizontal, put in two push pins, put the bike on the the tray, and insert two aluminum bar to clamp the bike down. Easy.
Unfortunately that rack only holds two bikes. I need one to hold three bikes. Looking around I see racks for two and four but not three. I found one made by Saris but it looked like pairs of giant crab claws.
Anyone can recommend a good hitch mount carrier, with the trays, that can be easily dismounted and swung out of the way when not in use, and can carry three bikes?