What exactly causes clicks and pops on vinyl?

Agree w/most of the above. So with your budget, here's what you do"

Buy good liquid cleaning system from either Walkeraudio or Audio Intelligent. Get good velvety-surfaced cleaning brushes(Disc Doctor or Mobile Fidelity).
Buy a couple of large white thick cotton bath towels.
Buy a plastic dish drying rack from Target/Walmart.

Place the clean towels on a large table. Clean by hand per intructions. Air dry in the dish rack. You can clean about 10 LPs at a time, in about 15-20 minutes, and they will dry in another 15 minutes. Place the clean LPs immediately in a brand new good sleeve(search archives or just go to Elusive Disc).
When about to play LP, swipe it with an Audioquest Carbon fibre brush to remove static and stray debris.

This isn't perfect, but it will get you surprisingly far until you can get a vacuum cleaning machine. Cheers,
Spencer

At the time of pressing, release agents are used that can/will collect dirt from the atmosphere and the cheap paper liner records come in. That's why it's good to use one of those nice record cleaning machines before ever playing the disc(bought my VPI back in the day for $325.00). When your stylus winds it's way through the groove, it actually melts the surface just as skates do to the surface of ice(just talking a few molecules here). If not cleaned prior to play- particles of dirt will be welded to the groove walls. These of course make noise and wear your stylus. Before I ever played a record(usually tried to find virgin vinyl pressings, MFSL, Crystal Clear, Sheffield Labs, Telarc, etc), I'd use the VPI, treat the record with L.A.S.T. after drying, let that sit awhile and finally: use my Discwasher brush on it. My records are stored in rice paper liners. Cleaner than paper, and they don't leach the elastomers out of the vinyl. Sound anal? The records I purchased over twenty eight years ago are still pristine, and I've gotten excellent mileage out of my styli. At very least: find a Discwasher brush and liquid, clean your discs b4 each playing, and don't scratch(OUCH) or touch the grooves with your fingers as Pbb said.

i have an extensive collection of albums, many 30 and 40yrs old. i clean my records and experiance very few infact almost no pops or clicks. i suggest you invest in a quality RCM you will never look back, the only reel tweek that works every time(assuming the record is not damaged).

The above comments pretty much explain why you hear clicks and pops and sometimes a continuous "swish" when you play a record. But it is wrong to attribute it all to careless manufacture and sloppy user practices. The origin of the problem really lies in the technology itself. Recording of sound by mechanical grooves engraved in wax (by Edison) or vinyl today requires incredible precision, and the result is fragile and subject to contamination. Any technology which is so dependent on perfect execution is undesirable. Good technology works well even when you abuse it.

The clicks and pops were never an issue when records were played with acoustic gramaphones (those things with big horns) or early electronic players. The sonic quality was so bad for other reasons, that the clicks and pops were the least of the worries. Today the playback equipment has vastly improved, and every little defect in the groove is faithfully reproduced. Also our expectations regarding sonic quality are much higher. We have taken Edison's invention to its ultimate limits, and the defects which reamain are inherent to the technology.

An analogy might be the typewriter. Over more than a hundred years typewriter machines were vastly improved, perhaps culminating in the IBM Selectric with the type ball instead of levers. Typewriters could go no further. Then came word processing on the computer. The old mechanical character striking device was obsolete in a decade.

Sic transit gloria.
.

As an addendum to all the truths above, if an LP has occasional, RANDOM clicks or pops then a wet cleaning/vacuuming that includes an enzyme soak step will usually remove most of them.

The enzyme solution from AIVS is very effective. MoFi has a new one in beta testing and my early results seem good. The older Buggtussel Vinyl-Zyme solution is effective, but less so.