I am just repeating what everyone has said, but welcome on board! The only downside is one more person to battle for OM gear with on eBay and such, haha. I should just be selfish and say 'don't do it, OMs suck' but I can't lie!!
As you have read, the 2n is great as are most of the single digit OMs. The ones that can eat batteries have been noted. The OM1 was set up for mercury batteries so that needs to be taken into consideration. Lots of options for that but I am doing the low rent option of a hearing aid battery and a wad of tinfoil;-)
I also have my original OM2 from back in the day. It needs its foam replaced in the prism before any more flecks appear on the viewfinder. Really I do not see a huge difference between the 2 and the 2n. I know there are ones. I got a 2n just because I knew it would be newer.
I have never tried the 2sp or the 3 or 4. I may someday but to me the 1 and. 2/2n are what I gravitate to. Some people speculate that the 3 and 4 may be harder to keep running for a long time as they have more electronics.