Welcome to the board! lots of smart, experienced, fun people here. The opening part of the Dierk Bentley song has tremelo as the major effect. You'll also want to tune your low e down to d (didn't figure it out, just a guess at thinking about the song) your amp may have tremelo on it.... if not.. there are some great tremelo boxes out there.... imo the best is probably the demeter tremulator... really nice and worth the money, the voodoo labs tremelo is also very good (I own one of these and have been very happy) and on the el cheapo side the danelectro tremelo will work (cheap and noisy)... the groovy way to have a nice trem and save some money.. if you can solder, the BYOC trem is great.... I built one and gave it to a friend as a birthday present (he turned 40) they are great quality and sound good.
for reverb, your amp may already have it, if not, it seems like lots of people like the Holy Grail reverb (I like the little guyatone H2 myself) but you can also pick up alesis microverb's used for 50.00 and they are nice, for compression, I've heard raves for the Barber Tone press, I have an old MXR dynacomp... I mostly only play country but I don't use my compressor that much.... most guys do especially for recording... it isn't a have to though... imo....
again, welcome to the tdpri and to country music! we need you!
"Idiots will be idiots. Let 'em. The world is 98% goober anyway." -A Famous Disc Jockey