You lose nothing by only playing the original games by the original studio. Go for it.
Reach is the only one I missed so I’m looking forward to this quite a bit.
PS - Mandatory “Halo 5 is a pile of shit” comment. 4 is ... okay.
Oh I want to play through all of them in story/lore chronological order (for the millionth time) including Reach, ODST, Spartan Ops and the 2 Halo Wars games but it's too early to play them now, I want to wait until Infinite is about to be released, play them all and then roll into Halo Infinite.
I most definitely wouldn't want to skip the 343i Halos as I liked the campaign in Halo 5. Was it the best Halo ever no, but I still enjoyed it and liked it quite a bit, and Halo 4 is my 2nd favorite Halo after Reach. If I was going to skip any of them it would be Halo 2 since it's my least favorite Halo.