For a mobile radio that covers almost all of the ham bands, HF, VHF low and high, and UHF, the Icom IC706 MKiiG is the best. can be tricky to program with limited menus and the audio is tinny, so an external speaker is good. Costly. widely available used for $400-600.
For VHF and UHF mobile, I have found the Alinco DR series (DR-135, DR-435, etc) to be hard to beat. Easy to program, powerful, wideband RF transmit stage, intuitive controls on front and also has many useful keys on hand mike. There is a model for 6 meters, 2 meters, 220, and 440 (70CM). start at about $150 new.
Alinco also makes an HF radio, the DX-70. I have one and like it's performance for HF more than the Icom.
All mobile radios can be used for base. Just get an electronically regulated 12 volt power supply.
Base-only radios are often much more costly but usually come with a regular 120V plug. Performance such as sensitivity, power, and noise is about the same, but base radios may have more technical but less often used features like tunable input filters, etc.
I do not care much for handhelds and I prefer single band units. Too many little confusing multi-menu buttons!! So I will not comment on them, except for a complaint on the kenwood TH-F6 which I own. It is a great performing and high-featured radio, but on high power, the RF will get into the speaker-mike and crash the radio's software at times.