Up above you asked about "VLP" sprayers. I know alot about "HVLP" (high volume low pressure" sprayers. For your job they would work out pretty good. However, you will have a whole bunch of masking to do. Personally I would mask off my edging for hand applying conditioner and stain. Then mask off all glass and drywall back aboyt 2 fott from spray lines. Drop a mask film over door into house, open door to garage and put in a box fan to suck out fumes/exhuast, then put a tarp down on new tile, and one out into garage so if you drip you don't track it.
If you have a Sherwin-Williams close by - they rent equipment - rent a CAP9100 HVLP and pot gun. Tell them you will be spraying (oil bases I hope)
so they can make sure the right tip and needle are in. Whatever your final fish is to be I would suggest at least two coats of gloss. Then sand and tack. Finally one or two coats finish. The reason for gloss is anymore it's cheaper than a sanding sealer, it won't build up a milky film like satin, and it actually sands easily! I like the purple Scotch brite pads for between coat sanding, conforms well to angles nooks and crannies. Holler if you need tech support or advice (Dennis Cook -
dejaco@bresnan.net) if we need I can give ya my home phone and talk ya through most anything. Just an offer - not trying to tell ya what to do! Anymore the contractors just send all windows, doors, jambs, base, case, and assorted trim pcs to my shop and we do it there (only have to go on site to fill holes, and final coat!).