VHF/UHF FM I'd go with any of the popular NO GROUND PLANE antennas like Comet or Diamond (I also build my own ngp's but I'm not going into that just now.
SSB, be it hF, VHF or UHF nothing beats a dipole for the lower bands.. A multi element beam for the higher ones.. HOWEVER...Anything over about 20 meters (By over I mean wavelength not frequency) Dipoles are not practical for RV use'
What I use with my TS-2000
HF, all bands. Ant-1 (I think) is a Kenwood KAT-1 Marine grade Auto-Tuner mounted on the rear of the RC.. I have multiple lengths of wire.. a 50 foot runs up a telescoping (Black widow) Fishing pole from Bass Shops Pro.. THen across the top of the RC (About 10 feet above the rig) to a Sunsetter Telescopign Flag pole.. Not my best antenna
Where parks let me.. I have a longer (Around 80-85 feet) Wire with aroudn 25 feet of nylon (non conductive no wire center) cord on one end.. The other end hooks to the KAT, and up the fishing pole. A 2 pound concrete "block" with a bolt in it hooks to the other end.. Allie OPP and over tree limbs.. I shoot for 20-30 feet or more up in the air. That's my best choice for 80/40 meters.
For 10-15-20 you might try a cobweb or most any of the newer multi band jobs.
Oh, I also have an Alpha (17' Vertical Whip with some added features.. Seriously NOT impressed with it. It is easy and fast to set up. but at best it is half the antenna the 50' job is (Based on S-Meter readings) I did finally get it up to minimum usable configuration but I would not recommend it as your primary antenna. Good back up though.