Yes anti stat inners will be a good investment, I use the ones from MoFi, they seem pretty good but there others available.
If the record is received with any form of printed insert I keep the inserts as they are integral part of the package, I tend to have the record in the anti stat sleeve alongside the the printed sleeve inside the outer sleeve. Some LP's are supplied with a good plain lined inner sleeve which can be used.
I have also invested in some outer sleeve protection in the form of resealable poly sleeves which help keep dust at bay, albeit I am trying out some new outer sleeves which have a pocket for the LP to sit outside the main sleeve, not 100% sure if this is a route I want to go down long term but the quality of these new sleeves is very good and much better than the ones I have been using.
Why outer sleeve protection? Well back in the depths of time we owned two cats and they decided one day to use my LP's as scratching posts, so many of my old LP's have very sorry looking outer jackets and some are just about holding together inside these protective outer sleeves.
What I do maybe a bit OTT but with the price of Vinyl protecting my investments as best I can seems logical, at least it does to me.