If you just need a transport, I would not worry about which model; "the sound" of a digital reader is beyond comical.
As you are budget-constrained, I would focus on gap-less playing (may depend a bit on what you listen to), regardless of whether it is a CD player (with internal DAC) or transport-only. If you like price-look-formfactor of something you see, check reviews re gapless playing. Most CD players have a digital out (check!), so if you want to maximize flexibility down the road, maybe get CD player and use digital out to your DAC.
Another thing to consider is that a "transport" by its very nature is "audiophile" targeted, therefore, likely overpriced for what it is. On second hand market, there are WAY more CD players than transports, which will also have effect on price/value.