Linear interpolation (bad)
Pick the nearest source samples and interpolate linearly. Cheap. Massive aliasing artifacts. Acceptable only for non-audio applications (logging, control signals).
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Sinc-based (correct)
Convolve with a windowed sinc function. Mathematically the right answer for bandlimited signals. SoX, libsamplerate, sox-libresample. Cost: ~100x linear. Used in pro audio.
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Polyphase + Kaiser window
Decompose the sinc filter into N polyphase sub-filters, one per output phase. Compute only the needed phase. Same quality as sinc, ~10x faster. Standard production technique. Most modern libraries use this.