Baits: The most effective, instant, cheap, out the can bait you can deploy in your quest for carp would be sweet corn. Right out the can. This will certainly get you on the carp, and other nuisance fish (trout, catfish).
Once the carp get wise to your corn offerings, you can start to introduce flavors, spice, salt, both are great carp attractants. Other baits that can be effective, night crawlers, bread/dough, nuts (just soak/cook em first so carp can digest/process them easier), boilies (there are more boilie recipes out there than there are people to look them up on the web!) if you wanted to give boilies a try then a quick internet search can provide you with ready made, or recipes to make your own, maggots, any larvae/worm etc.
Line: My personal preference is monofilament as mainline. 8-12 lb test is a good starting point (15-20lb if you are fishing snags for abrasion resistance). You do want to ensure you reel can hold a good hundred yards+ of the line as a carp can easily spool you if you are not careful. I used to use fluorocarbon mainline - it sank better than mono had less visibility. Given the cost of flouro I now moved to just using it for my hook link. I will be using braid this year, in very weedy conditions only note of caution is with 0 stretch on braid careful playing of fish could be needed to avoid hook pulls.
Reel: Any spinning reel with a VERY good drag that can hold 100 yards of your preferred line or more. You can either play the fish with the drag on the reel or back winding I know folks that do both. Back winding does avoid the line twists but a real good drag will save you more often than not.
Rod: Any medium heavy rod, 6ft or longer can do the job. You want a rod with the backbone for playing a large fish but with enough bend and forgiveness once the fish is close in to help with those last minute lunges.
Hooks: I use wide-gape micro barbed size 6-8 hooks many use circle hooks both can be very effective with arguments galore as to which is best. Just make sure its a very STRONG and sharp hook. Carp can easily bend out cheaper hooks.
So, get back out to that lake, get your corn stuffed onto that hook, lines cast out, and wait for the drag to sing !
If the carp are on the surface, perhaps try a piece of bread (floater), biscuit, heck, even a cheeto (anything that floats and is tasty) cast out near to them then slow pulled back in front ... aka dry fly with bread!
... and do post some pictures of your carp captures when they come ..
PS: Some days, no matter what you cast out there and offer, the carp aren't in the feeding mood.... !