Neatfish, that invert you found is just a regular bristleworm, relax lmao! they are good detritus eaters and a part of your CUC. that is the most common bristleworms species you will find in reef tanks, and you will find them in ALL SW tanks with live rock. they are not bad. NEVER touch them though. It will be very painful if you get stung by their bristles.
You usually want to let the tank sit and cycle for at least 2 weeks or more before putting in any life. be sure you're testing it and once its ready you can add stuff like you already did just now. make sure you have no ammonia, no nitrite and below 20ppm nitrates. once you start getting algae in your tank, your nitrates should drop to 0ppm and that's where you'll want to be at from then on. you want very low nitrates for a coral reef. but dont worry. corals help with that too. their symbiotic algae can use the nitrogen in the water.
Also i'd only keep one peppermint shrimp per 3 gal tank, but if you're not planning on any fish, or other large invertebrates (non-coral) then a pair of those things is ok for a while. eventually they'll get too big...i think. they grow to 2"+
looks like you got 2 of them, right?
how are you topping off the tank? and is your salinity staying constant at around 1.025-1.026 SG?
Found a pic of some of mine:
I had more than 50 of them in my picotope after a while. when you get to the stage of feeding your whole tank, you'll get to see quite a show of all the inverts getting out of the rockwork to try and get some grub :P
but that's far away. you don't need to feed the entire tank until its full of coral, and is mature. so don't worry about it for now.