If you're only interested in audio, a good quality 24 bit/96 KHz sound card and proficiency with Octave or MATLAB is probably the best price-performance.
What that won't get you is someone else having done all the hard thinking for you. It will require mastery of DSP and the use of the Fourier transform. "Random Data" by Bendat and Piersol is the best reference if you have learned calculus.
You don't say what you want to measure, but as an example consider this.
The task is to measure the transfer function of an RIAA preamp.
Write a program which feeds a set of known signals to the DAC of the sound card and record the ADC output using a cable from the input to the output.. With two outputs and two inputs you have four equations which you can solve for the errors in the two DACs and the two ADCs. If you take a long recording and autocorrelate it you can get the amplitude spectrum of the combined transfer function of the DAC & ADC to whatever resolution you want. Once you have calculated the corrections, put the preamp in between, adjust the levels appropriately and measure.
You won't get the answer as easily as by spending a bunch of money. But you will know a lot more.
Search online for "Max Wein, Mr. Hewlett and a Rainy Sunday Afternoon" by Jim Williams. There's a thread in the forum about building a Wein bridge oscillator which has additional information.
Have Fun!