As for the actual cable, at the frequencies and lengths you are likely to use, I would suggest an RG-58 cable with 50 Ohm BNC connectors on both ends. RG-58 is probably the most common type of 50 Ohm coax cable out there (also commonly used for 10base2) and reasonably sturdy. It is not the most flexible cable, or the best shielded, or the lowest loss, but none of them should be terribly important for your application. You are not sending many Watts of power across a long cable to an antenna somewhere way up a mast.
Make sure you do not buy 75 Ohm cable (e.g. RG-59), as is commonly used for video applications.
Yes, if you want to connect your function generator (which will almost certainly have a 50 Ohm output impedance) to your scope, you either need to set the input of your scope to 50 Ohm instead of 1 MOhm (back in the Tek 2225 days this was mostly limited to higher bandwidth scopes, so I would guess the 2225 does not have that option) or use an external terminator.
The 50 Ohm feed-through terminator that Dave showed around the 7 minute mark is basically the same as the BNC tee and 50 Ohm terminator used in the 10base2 days. However, as you can plainly see, putting a tee creates a 'stub' from the tee to the scope input. As Dave discussed in his video, having an unterminated line results in reflections that can distort your signal. This stub would do the same at frequencies above 50 MHz or so. Hence the more compact feed-through terminator which is good up to about 250 MHz. Because feed-through terminators are quite niche (mostly used for this exact application), they tend to be quite expensive ($30-$50 or so last time I looked). For many applications the cheaper tee + terminator works just as well.
In addition to the cable and some kind of terminator, you might also want some way of connecting the function generator to your circuit, which may not have BNC inputs (e.g. a breadboard). There are various solutions, like a
male BNC to some kind of grabber cable,
male BNC to banana plugs,
female BNC to grabbers that you put on the end of a regular BNC - BNC cable, or you can put
one of these on the function gen and use banana leads. If you want to be cheap, you could even just grab a
female banana jack and clip / solder some wires to it.
For low frequencies anything works fine. The higher the frequency (or the more sensitive you are to noise and interference), the more important it is to keep things in a coaxial environment for as long as possible, so in that case you would not run long banana leads from your function generator but convert to flying leads as late as possible. For a beginner I would probably just convert to binding posts for convenience. I like to use the short breakout leads with female BNC connector and clips or banana plugs on the end because they are modular.
There are other manufacturers than Pomona and many of them you can order from China for much cheaper, I just used Digikey for convenient links.
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