The resistor is for keeping the load (PC audio input) from possibly loading down the source (tapped radio's discriminator) while the cap is primarily for DC blocking - keeping any DC voltage present on either side of the tap (source or load) from interacting with the rest of the circuit. Ideally, you only want to pass and deal with the audio ac signal so you don't want to pass any DC. Some discriminator taps on some radios may have DC present and some PC audio cards might not deal with it well; so, to be safe, a DC blocking cap is a good idea as far as blocking DC is concerned. The non-ideal problem with the cap, however, is that it creates a "filter" together with the source and load impedances and any other series impedance such as a series resistor. This filter effect may help you or hurt you depending on what type of signal you are dealing with. Ideally, to yield completely raw discriminator output across the whole audio range (including sub-audible signals) you don't want any filtering (in the tap circuit) so as to allow the software to have full access to all possible discriminator output. In some cases, though, filtering can help but then you should really know exactly what the load and source impedances are so as to calculate it properly. The series cap in a basic discriminator tap is not really intended as a true filter with unknown source and load impedances, etc., but some filtering will occur. To keep that to a minimum, ideally a larger value is used, but the non-ideal characteristics of common electrolytic caps will cause them to become inductive at high values. This is not usually a problem at audio frequencies, depending, again, on the source and load impedances, but it should be kept in mind.
For most discriminator taps, a value of 1uF to 10uF is fine and is not terribly critical. You could get a few caps with values spread throughout that range and try them each to see which gives you the best signal for your software. Ranges in the 1uF to 2.2uF range can also be accomplished using ceramic caps which are inherently non-polarized and so can be inserted in the line without regard to DC polarity unlike common electrolytics which have a polarity. The most positive DC voltage point should have the "+" terminal, of course, usually that being the source. There are non-polarized electrolytics as well and there are special very wide range DC blocks if you want to spend the money and have the widest range possible with no DC passage (Mini-Circuits has them). Generally, if you want to pass very low frequencies as clearly as possible then you want as large a value cap as practical or no cap at all (or else a special DC block with wide range). The higher the frequencies needed the less the cap will have an effect until the non-ideal characteristics begin to manifest themselves.
In many cases, using no cap and even no resistor works fine. I do this with my old Radio Shack PRO-2052. But, to be safe, especially when dealing with an unknown source and load it might be best to at least put a resistor inline (4.7K to 10K ohms is common here, as you have seen). You can always measure how much DC might be present at the discriminator tap of your radio with a multimeter - if you see a steady DC bias with no signal present then, well, you know it is there. Whether or not the DC will be a problem depends on your particular PC sound card/audio input circuit design.
-Mike