Kevin- In addition to what has already been said about cleaning records, aligning the cartridge and maybe upgrading your table/cartridge, a DBX 3BX running through the tape loop would yeild pretty good results with your current table/cartridge noise issue. If you upgrade, the 3BX becomes less of a factor as the noise floor of the upgraded table/cartridge drops.
Also, as someone mentioned earlier, there were several "tick & pop" eliminators manufactured such as the Burwin TNE 7000 and a couple of models from SAE. Again, if you upgrade, there won't be much of a need for this kind of signal processing. (My TNE has been in storage for 15 years, but I still have occasion to use the 3BX.)
And, much as I fear weighing in on the LP vs CD lunacy, it's notable that, from a strictly sonic (the music only) standpoint, most "experts", including CDP makers, have concluded that analog sounds better. (Many CDP makers strive to sound like analog and claim their product "sounds almost like analog" while exactly zero turntable makers attempt to "sound almost like digital".) I suspect alot of folks take issue with this fact because they mistakenly think that "sounds better" is an all-encompassing phrase which means that "analog is always better at anything and everything all the time" which, of course, is not true.
LP's are more work and they are not as convenient to play as CD's. And, if one prefers to listen to numbers on a page(something I gave up doing 20 years ago), CD's can sometimes have a "better" S/N ratio and dynamic range. CD's can also sometimes be quieter between tracks or in quieter passages. CD's don't have "ticks and pops". CD's are getting better. Etc, etc, etc. (BTW- Analog is getting better, too- ALOT better.)
Obviously, many have had great experiences with analog and find it to be worth the effort. Your mileage may vary. If you need help, there are alot of very knowledgeable folks here for you.
And, yes, for the record, I do have a fairly good CDP and a whole bunch of CDs that I listen to and enjoy frequently.
Regards
Jim