Sadly I think that I have too much experience with varnishing. My previous boat was a classic trawler with teak everywhere.
In the course of caring from my previous boats hand rails, cap rails, doors, window frames, hatches, etc. I came to the unleasant conclusion that there is no substitue for an amazing amounts of effort.
I used varnish strippers in the past and ended up having to redo portions of my awl-grip. Hence no more strippers were allowed on the boat (the other kind was NEVER allowed either

). I was given some bad advice once about using a brass brush. Since teak has streaks of "softer" wood, those soft steaks get lifted out and you never can get that smooth finish after, or not without sanding your teak away. Hence no more brass brushes.
I use a orbital sander with 60 or 100 grit to get the old varnish down and then use successively 150, 200 and 320 on my 1/4 sheet pad sander to get it down to smooth. The goal is to get rid of the old varnish, not the teak. I like to use teak cleaner and brightener to act as a process check to see if I missed any spots of varnish as they show up as "splotches" when the rest of the raw wood is wet with the cleaner and brighter. If you miss these and start laying varnish they show up as a yellow patch and, I think, spoil the look.
Tack cloth the heck out of it and start laying varnish.
I always start with a coat of 50-50, 50% varnish and 50% varnish thinner to act as a sealer coat for the raw teak. After that, 5-10 coats of 95-100% varnish, my personal preference is Epifanes. I use 320 grit between my coats with very liberal use of the tack cloth to get the wood as clean as possible prior to the next coat.
I'm doing my wing doors right now as they were a bit rough when I bough
fun@sea.calm. On my wing doors I have an interesting configuration of screen door, that opens out along the companion ways and a solid door with the typical glass window that opens into the aft deck area. I haven't started my screen doors yet which I'm expecting them to be a bit trickier as I cannot get a sander anywhere near the screen / mesh without ripping it.
Still my 56 has only a fraction of the teak that my 44 trawler had. I'm happy to only spend only a fraction of the time caring for the teak that I used to have invest in my old boat.