I'm kind of in your situation because I just started gigging again and decided to start using pedals. I've been playing for 25 years or so, but never used anything but a tube screamer. I usually play through Marshalls, too, but they're older and probably cleaner sounding than the DSL. Anyway, here's what I'm finding out.
I had a volume/wah that I hated (one of the Morleys). It uses an opamp to do the wah thing, and I only wanted it for Volume, but both sound kind of harsh. I got another wah (w/o Volume) that uses a more traditional inductor and I love it (first generation Budda) - more watery/buttery sounding, and not harsh. Stays on the board.
I wanted fuzz, and I like the old sounds, so I got the Fulltone Octafuzz. It's really moody and can sound like hell if the rest of the chain isn't right, but now that I've learned it a bit, I dig it, and it's staying on the board.
I had previously destroyed my TS-9 tube screamer, so I got a couple of TS-9s off ebay, but they sounded bad to me - I replaced the opamp in one, and it sounded better, but still kind of fizzy - not on the board.
I got a couple of DS-1s and kept one stock - hate the stock one - too fizzy and blurry sounding for me. I modded the crap out of the other one, just replacing capacitors, resistors, and diodes with no real sense of direction. Eventually, I liked the sound a lot better, but it seems to have a very narrow range of usable application (with regard to guitar gain, amp, gain, etc. - i.e., picky one-trick pony) - not on board, but may go back.
I have a Fulltone Fulldrive 2 (prior to the mosfet model). With my JCM-800 with the preamp set to about 5, it sounds great - real nice solo sound, and it's off for not soloing. But when I cleaned up the amp sound by turning down the preamp on the JCM-800 or going through an older non-master volume marshall, it sounded fizzy and stupid - not on the board.
I paid a premium for a "Timmy" overdrive pedal on ebay (ostensibly signed by the Cochrane guy who made it, but I have no idea if that's really his sig), and I think I'm done - works well with both overdriven and clean amp sounds - searing blue LED (bad for me) -- staying on the board.
Boost - started with a homemade one I got in a pawn shop - may go back to it, but it seemed to be flubbing the low en. Got an EH LPB-1 - sounds great, has way too much boost, but you can turn it down. Staying.
tuner - got a slimmed down TC Electronics polytune - love it.
Those are really the ones I use, but for good measure, I kept going.
Chorus - I hate chorus, but I want to someday play Purple Rain if I can surprise our singer on stage and he has to sing it, and I need it for that. Started with the Boss CE-5 - it sucked tone whether it was on or off - not on the board. Went to the EH Clone Theory - thin and harsh - off the board, finally got the TC Electronics Corona. It does not suck tone, and, as choruses go, sounds pretty good. Stays on the board until I realize I'm never actually going to turn it on. Can be configured as buffer or true bypass (currently true bypass), so may keep it if I need a buffer, which I don't right now.
The guy at the store recommended the Black Cat tremolo - it's nice, even though I'm not sure how I'm going to use it. Nice clean boost if the tremolo turned all the way down, so it could probably fill in for the LPB-1 (with much less boost, but enough for me). Probably staying on the board.
Delay - using the Mojo Hand Recoil - sound pretty good I think, but I'm not sure what to do with it. Has a searingly bright blue LED, which is a minus. Probably staying on the board.
I had a guitar with nice tone but no sustain, and so I got a Keeley two knob compressor. It worked for this one recording, but, as has been noted, I freakin' hate compression. It has a trimpot to adjust the attack function and I turned it all the way off (to preserve the attack), and still didn't like it. Depending on your sound, a compressor might be good, though - it just has no place for me. I got a fret job on the guitar, and now it sustains much better (wasn't expecting that), and the fuzz and OD also add to sustain, so I this one's not going on the board.
By the way, those saying that you (and I) are going about this the wrong way are absolutely correct - much better to take it slow, study up - try out with *your* rig, etc., but I totally understand the impulsiveness that defeats doing things the right way, because I has it.
Subtle changes in the signal coming out of the guitar, impedance, harmonics, strength, can have wildly huge effects on the pedals - especially fuzz. Since all this is in play starting with your pickups and including your playing style (the most dynamic factor) and even your cable, your mileage may vary significantly - even with the exact same rig on different days if you're playing differently.
On the other end, different amps are picky or not in different ways and at different settings, and will respond well or poorly to the signal they're getting, which started out skewed due to your playing and pickup, and then got a lot more skewed as it went through your signal chain, etc. Add all this up, and you can get a sense of the scale of the problem of recommending pedals on an internet chat board