To measure active circuits, you can use a 10X oscilloscope probe. This can protect your SA input. You can also use the probe with the GND attached to the tip as a "sniffer" or small antenna to find the signals given off by active circuits. You can characterize a probe by just putting it into the circuit, from your SA generator to SA input, I did this and I was surprised that the trace was relatively flat in the frequency range of the probe. If you have a suitable scope probe try it on your SA using the generator on the SA. You will need N to BNC adaptor for this. Again, this works only in about the freq range of the probe, but can be quite helpful.
Most of the time you probably are not concerned about the exact power of the signal, but the frequency is of most concern, you will see the frequency desired and any spurious freq also.
Measuring the real output of active devices like amplifiers will require attenuators, possibly ones that can deal with several watts. I do this all the time but I have a setup that puts all the power thru attenuators for radio testing. My usual attenuator handles more than 100 Watts.
Shabaz advice is good, I use some RG 58 cables and the smaller 316 ones are definitely easier to use, most of the time. The SMA to N connectors will probably stay on the SA almost all of the time, so get good ones, the SMA connector side will get a lot of use.
Sometimes you can pick up used connectors since a lot of these adapters are used by cell tower service people.
Your idea about starting with passive devices like filters is a good one, you will not overload your SA input. Remember that you are measuring the characteristics of hot only the filter but the connectors and if the filter is on a board the characteristics of what is on the board.
I needed a SAW filter for a project and was surprised at how inexpensive some of these are on e bay. Just a suggestion.