Don't skip any of them, all mainline games are great, just start with the first game, install the mod that removes the door transitions and switch to analog stick controls and you're good; you can skip side games like operation raccoon city.
You could also somewhat skip zero because the item management in that game goes a bit overboard, and it's not really referenced in other games ever again; definitely do play revelations, after re4, and revelations 2, after re5.
RE5 can be played with traditional tank controls, but it also has a setting that allows strafing, which was the default for the x360 release (because of the gears of war crowd), however it's the last game in the series where you can't move and shoot, but you'll get used to it quickly; at least the zombies aren't bullet sponges like in re2 and the melee attacks are super satisfying.
The first dlc, lost in nightmares, also has a neat hidden feature to change the camera for the first part of it to fixed, instead of third person, so it looks like playing the first game.
RE6 is a gigantic game, because it has 4 different campaigns that mimic the feel of several different games.
The leon campaign is more like re4
The sherry campaign is more like re3
The chris campaign is more like re5
The ada campaign is more like re2, this campaign was a secret and the only one not playable in coop, but people complained so capcom patched it so it's playable from the start and in coop; do not play it in coop and save it till last.
I doubt many people are still playing it now, but RE6 also has this unique coop feature during several chapters; in some of them 4 of the main characters will be present because the campaigns overlap at those points, if you are playing online during, the other 2 characters might be controlled by other random players instead of AI. This same method was later also used in DMC5
RE7 is quite a departure from the previous games but is still very cool, it starts off pretending to be supernatural horror, but halfway through it starts going back to conventional RE stuff.
RE8 is basically RE4 but in first person, it has a 3rd person mode now, but the game wasn't really built for it, with all the door/wall peaking and such but it's still a great option to have
I tend to analyze games as I play them, some kind of habit I have because I enjoy it. This is why I would most probably always start with the first game, even if that brings my back into the 80s lol. In particular, this helps understanding what features each entry has brought up to the table. Often, the foundations of an excellent entry were there on a previous game that isn't always remembered as fondly.
