Well, the first thing you need to consider is if the amp in question would really benefit from an op-amp upgrade. IMO the better things to replace first would be capacitors, especially electrolytics - these tend to dry out over time and lose capacitance. Replacement with the same value is to be preferred in case the purpose of the cap is not exactly clear (these do appear in frequency shaping circuits - like tone controls/equalisers/etc and changing the value would lead to a deviation from the intended behaviour). Higher voltage rating is usually fine as long as it can fit onto the board.
Coming to op-amp upgrades, expensive or high-speed or otherwise exotic replacements might not necessarily make an improvement. Bear in mind that old equipment might not have the necessary circuit layout or compensation schemes that modern (or high-speed) op-amps need - this can cause the new replacements to behave oddly when put in (oscillations, for example). Slower op-amps are more tolerant of circuit layout than high-speed ones - where the slower one worked happily, the new one will oscillate, if the layout is such.
From personal experience... I had built an op-amp based power amp using the LM348 (quad 741) - this worked very nicely and was stable till I replaced it with a TL074 quad device (both ordinary and cheap ICs, but the TL074 having a much higher slew-rate) and there was oscillation. I had to tame it using a cap between the op-amp's o/p and ground - crude but it worked that time. This goes to prove that even between perfectly ordinary op-amps, simply swapping in a faster op-amp might not always work.
Also, check pin-compatibility between the originals and the replacements - some op-amps, especially dual op-amp packages have differing pin-outs between makes. And lastly, price would be the greatest determinant of which op-amp to use as the replacement and this needs to be considered keeping in mind that expensive does not necessarily translate to improvement.
