help me with cheap tape deck.

Why don't you get an A/D converter and burn copies of your vinyl? Kind of going backwards using a cassette deck. I have a Nakamichi BX-1 I bought at a garage sale for one dollar. I'll give it to you free if you pay the shipping. It will take about $125 to get it working...

Have you thought of a DAT deck? I have one in my system and I use it for digital(CD) and the analog inputs for vinyl. I saw a used one on audioshopper for 200.00. You can purchase 2 hour DAT tapes for around 4.00 or cheaper. The tapes are small and easy to store. Good luck.

do you need DAC for DAT?

No you don't need an external dac for a DAT player. They are like one box cd players with a dac section built in. DAT players have a digital out to use a dac if desired.

See if you can find a Nakamichi LX5. If you wanted to spend the $$, a CR7A would be better (automatic biasing, alignable playback head, and a few other bells & whistles), but the LX5 is very good. It doesn't have analog VU's, but with cassette that's a benefit, not a detriment. VU's read average levels; what you have to be concerned with when dealing with cassette is peak levels, and the Nakamichi meters do that just great. I have both units, so I can attest to their quality as recorders.