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.
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I think it certainly can be a good decision if you purchase for the right price taking into account tube replacement and replacing/upgrading parts as noted by lowrider. BTW you mention the SP15, do you require a phono stage?
For $2-3K you can get a really good used tube pre, especially if you don’t need a phono stage. But even if you do. Not to disagree w my esteemed colleagues, but most tube pre-amps (with some notable exceptions) are very easy on tubes, so I would not necessarily believe that you would have to budget for replacements. Even if you so, there are many good new stock small signal tubes available w/o breaking the bank. There are lots of good ones for sale now; in addition to the CJs and ARCs, there are models from Audio Note, BAT, and Modwright available well within your budget.

BTW, it's my opinion that a good pre is the heart of a good system, you can't go wrong here with getting the best you can afford. 
I like my ARC LS-25 Mk II, which ocst $2500 with new tubes used from a dealer.

You can get different sound than ARC, but it is not clear to me that you can get better sound.

Other options include CJ (phatter sound)

or maybe Primaluna tho cost may not fit your requirements.

I like to stick to companies with established track records, good support, and a history of long development towards some euphonic goal.
I've owned a melos 222 preamp for about 20 years. I had it looked at last year and upgraded some switches, the volume pot, umbilical cord, added an IEC, etc., to great result. Although it's not the level preamp you're looking for, my point is that it's worth upgrading old quality equipment, if you like it.  
After I purchased a 2nd Accuphase C275V, I find that it grade in sound is unable to compare with the pre-amp. I owned more than 30 years ago.  The problem is the old tube amp. has problem occasionally which required maitenance which is trouble some for me for I am not an engineer. Without comparison, you don't know how good my old tube is. The SS's slim and lean sound reproduction makes me tasteless.