With your budget you can pick at the top of the heap if you are willing to go a little older. ARC SP-10 or SP-11. While they are harder to find, there are even CAT SL-1s available in your price range. I bought a used CAT SL-1 over 25 years ago and have never been tempted to upgrade it. In all those years I've only had to replace one cap in the power supply. Ken builds them to last.
It is a good idea to purchase a vintage tube pre-amp.
Since the new one are pretty expensive and what I can afford is an old one with budget of US$2000~3000. Since I don't have much knowlege on electronics, but I have authentic listening capabilities. Is it good idea to buy an old gear of tube pre amp. around 10 or 15 years such as Audio Research SP-15 or something similar (the newer one within my budget is better of course). I would prefer a stable, long time use gear without much trouble.