Limit screws limit. They have no effect on indexing. The start point for correct indexing is actually the second smallest sprocket. Get that right and . . . happy days. Set the limit screws (with the cable still in tension) so the chain can drop onto the smallest sprocket (but not further) and so the chain can climb onto the largest sprocket (but not come off towards the spokes).
HTH
I open up my limit screws prior to indexing and then set them once I'm happy with the shifting. This prevents me from confusing limit stops with cable tension settings. I set the front limit afterwards by tightening the screws until the mech rubs the chain and then back off a quarter turn or so. The rear mech I set by tightening until I hear noise and then backing off until the noise goes.
The first time I indexed the front, I set the large ring limit a tad too tight before indexing and I ended up over tensioning the cable trying to force the mech over the the large ring making it hard to get my grip shifter to click into the 3 position. Setting the limits after indexing prevents this.
I also try to make sure I have a couple of turns left over in either direction on both barrel adjusters so that future adjustments can be done using just those. Generally, a quarter turn either way is all that is needed for a fine tune.
Not sure if it matters, but when I park up the bike, I don't leave it in gears which keep the cables fully tensioned?
Shimano provide very good online dealers manuals for their components which walk you through the full installation procedure and if followed to the letter, leave your indexing faultless. I'm fitting a new front mech this weekend and it has big ring spacing guide and a removable alignment block to aid installation. I'm quite looking forward to doing the job.