The bass response with a tube preamp depends on the output impedance of the preamp and the input impedance of the connected amp. Using the worst case output impedance (not the manufacturer's "nominal" value) with the 10X impedance matching rule of thumb is usually acceptable. Some people suggest a ratio of 20X or more.

I don't know why cost would be a factor. If the input impedance of your amp is sufficiently high, then you'll have many choices. So determine the input impedance of your amp, divide that by 10 and look for preamps whose worst case output impedance does not exceed that value.

The Stereophile web site is a good resource for this type of information. The Audio Research SP16 has a low output impedance and should work well with solid state amps.