MC---Al and Griffith gave you a lot of great info and advice, all of which I agree with. Here's some more!
Both the Nitty Gritty and VPI cleaners are good, and each has an advantage over the other. As Al said, with the NG the LP doesn't sit on a mat when it's being cleaned, so doesn't pick up dust (or whatever) from said mat. With the VPI, the LP sits on a felt mat as one side is cleaned, so when you flip the LP over to clean the second side, the just-cleaned side now lays on the felt. If there is any dust on the mat it can get on that just-clean side. I solved that problem by having a spare mat, which I put on the platter after I clean side one of an LP. That mat is reserved for already cleaned sides exclusively, so I wrote "cleaned" on it's bottom in felt pen. The platter of the VPI is what gives it it's one advantage over the NG---a work surface on which to lay a used LP to scrub it with a hand-held brush, before vacuum cleaning it. And I have a third mat just for used LP's, so as not to contaminate my new ones. And it's labeled "dirty", of course. Okay, maybe a little OCD, but I see you're okay with that!
Some of the LP cleaning fluid companies make a product specifically for removing the stamper goo from new LP's. You use it only once, before any other cleaning.
Regarding Last Record Preservative: I completely understand others' apprehension about putting anything on their precious LP's. I'm confident Last does no harm (quite the opposite, in fact), but it's always a good idea to exercise caution. Actually, it's value increases with heavily played LP's, so if you have records you're going to play infrequently, skip them. I know Walter Davies, the Last company owner/designer (he had a Hi-Fi store in Livermore, CA---I bought my first good system from him in '72), and the research he did on the preservative before bringing it to market. As for the increased noise after applying it to uncleaned records, what happens is the preservative bonds molecularly to the vinyl, pushing the dirt on the surface of the walls of the groove out of the way to do so, where the stylus of the turntable "hears" it. So yes, clean the LP after applying Last.
The anti-static gun I use is the Milty Zerostat, and my procedure is exactly as Al's, including not releasing the trigger in the direction of the LP the third and final time. What's that expression about great minds?!
One of the carbon fiber brush makers offers a version with a grounding wire, to drain static from LP's. That option is available for you.
New inner sleeves in a real good idea, as long as you get the Mobile Fidelity type. There are others that transfer "plasticizer" contained in their composition onto LP's put in them, as I found out years ago. Hopefully that type is no longer even being made.
Al's mention of the circuit of your phono amp affecting the amount and degree of LP surface noise is fact. The quality of your tonearm also affects the perceived noise level. The more non-resonant your arm is, the less it will "ring" when fed the sharp impulses from your phono cartridge playing groove defects.
I know this sounds like a lot of stuff, but once it becomes a routine it's no big deal. I'm not sure I would want to get into LP's now if I was young, but when you have four or five thousand of them (or more. My friend Brooks Berdan had, I don't know---at least 20,000, maybe thirty. He converted his dining room into his record room!), having kept a collection already amassed when everyone else "went digital", as some of use have, and having not gotten CD versions of many of those LP's, if I want to hear the music contained in their grooves, I have to do this stuff. I actually enjoy the ritual---most of the time!