TS-2000 very noisy receiver on HF, but pretty darn good on VHF/UHF except for some satellite channels have "birdies". Some claim they are excellent on HF, but I've owned several of them early and later. All about the same.
FT-857/897 (D) Actually a very good rig. Kind of flat sounding rx audio to some. Fairly heavy on menu's.
Alinco DX-70T(H) Probably the bargain of HF rigs. Good TX/RX audio, 160-6 meters. All filters built in. Very crappy noise blanker.
Yaesu FT-100(D) Again a decent radio IF you find a good one. I have been through three of them before settling on an FT-100. VHF/UHF finals are very hard to find and are a common failure. Some these seem to be just junk and others are excellent.
Icom Pro I or II Excellent rigs which are famous for their "panadapter". Very reliable overall. The Pro II to me has far better sounding RX audio than the original Pro.
Yeasu FT-857GX Older HF rig with about 8 memories, all filters, and overall not to bad of a radio. Famous with CB'rs as they are very easy to mod with a simple switch.
I own all of the radios above, but some I've owned in the past are the Icom IC-706MIIG, Flex-radio 1500 and 3000, FT-817, and the Elecraft KX-3.
The 706 was/is a very good radio. Fairly pricey for used ones, though the early models are selling for around $400 or so.
Flex rigs all seem to be good, but they are chained to your computer.
FT-817 is an excellent rig but only 5 watts on all bands.
The Elecraft KX3 is an excellent radio for QRP also, but is very pricey, and almost worthless to use as an SDR rig tied to your computer. The I/Q output has lots of images. If you want an SDR rig get a Flex or buy a good quality SDR receiver with direct sampling and tie that to a computer controlled transceiver.
IMHO why beat your self over the head with QRP? You'll end up wanting an amp eventually so people will hear you, especially on SSB. Get a rig with 100 watts or so and have fun.