Some advice please.... Limited $$ what should I spend on FIRST?

My Best Friend and I live together.  He has a KILLER Audiophile system centered around his Martin Logan 15A's.... I'm not looking to reduplicate that.

I will be using his Theil's speakers that are hotroded.  I intend on getting the ML center channel speaker and need a decent 2.1 Amp to drive the 3 speakers.   The choice I am struggling with is either spend about $2,300 on a 75" 4k TV and that will free up ~5,000 -6,000 on the amp.  OR  spend about $2300 on the amp and the rest goes towards a projector and screen.  Either way, the 2,300 will be a temp fix until I can save more $ to start filling out the HT system... I simply don't have enough $$ to get everything at once.... SIGH its always never-ending pursuit of upgrading lol
wait, enjoy your friends system, see what's around when you move out.
Because his audio system is in a listening room and I want to have a home theater in the family room
We do enjoy it daily but there is no video in that room and its not set up for that.

1st, Start with a ’front stereo system’ i.e. 2 channel integrated amp, with a unit that has ’HT Bypass’ INPUT.

2nd, the AVR needs to have pre-out. The pre-out will go to the ’front stereo system’ thru it’s ’HT Bypass’ input.

thus, the AVR only needs to be powerful enough to drive the center and surrounds.

the better equipment always drives the front l and front r speakers, for music (AVR OFF), AND for 5,1, 7.1, AVR ON.

AVR, when on, controls the volume of all, including the front.

I started this having it misunderstood, by the end it became clear:

Think NOW about the bass, either

large fronts with enough bass, or,

a pair of subs for ’stereo bass’ (front facing, adjacent to the mains, no ports or front ports) or

a single sub for dinosaur stomps.

where’s the crossover? if only ’front stereo system’ for music, where/when is the bass on? you would want bass always on, thus not using a sub in surround mode, or

adding a single sub in surround mode?

check out RAVEN, see their amp's built-in crossover, sends lows to self powered subs, lets the amp more easily handle upper bass, mids, highs, thus the 2 channel amp can be: smaller, lighter, less heat, more placement options, less money too.

any amp with 'pre-out' can go to a self-powered sub, then back at line level minus lows to 'main in', same except the crossover is in the sub, Raven's crossover is in the amp.

I think you’ll have a much more rewarding HT experience going with the projector and $2300 amp. Plus you can buy the amp used and sell it for little loss when you’re ready to upgrade to a better amp. I wouldn’t get an ML center to pair with Thiel speakers as they’re likely not a good sonic match. I’d try to find a used Thiel center or get an SVS Ultra Center that’s a great center speaker and probably a good match with the Thiels. And SVS offers a very generous risk-free trial period so if it doesn’t work out you can just return it. You don’t specifically mention a subwoofer (except you mention 2.1), but it’s not optional for legit and truly entertaining home theater, so while you’re talking to SVS consider picking up one of their PB2000 Pro subs and they might cut you a deal.

BTW, what preamp/processor are you planning on using with the amp? For an amp, one option would be a D-Sonic M3a-1200-3 that’s only $2375 new and would work great in an HT setup and have plenty of juice for power-hungry Thiels. It’s good enough that you may very well not need a future upgrade. Anyway, FWIW and best of luck.
What is the rest of the room like and what is the intended use? Is the room only for TV/Movies or is it a general gathering place in the house like a family room/rec room? What is the lighting? Are acoustic treatments an option? 2-channel music as well or just video sources? Room size/shape? Hard reflective surfaces like concrete, hardwood flooring, and windows? Which model Thiel speakers?

In my experience, a projector and separate screen is great for a dedicated home theatre, but in a mixed use room that will have significantly more ambient light, you might be better off with a large LED/OLED/etc TV.  Aside from the cost savings, you don't have to worry as much about the ambient light, line-of-sight, installing and running cables through your ceiling (I know ultra-short throw projectors exist, but are more expensive for a given picture quality and still best in dark rooms). Plus if you ever move, it's easier to take a TV with you to repurpose elsewhere if the new place doesn't have the option for a dedicated theatre space.

A huge screen may help to make you feel a part of the action, but the room has to be large enough for you to actually take it all in, and not all spaces are...its why the front row of a movie theatre isn't typically the best seat. Depending on the room size and seating distance, 75" might be plenty and splurging for a 120"-200" projection system might not necessarily make it more sacrilegious as that feels to say. If your room is big enough, I'm all for having an IMAX screen in your house.

As another post noted, I think you may have the lingo a bit confused and that could cause further confusion down the road. a 2.1 system means 2 front stereo speakers (front left & front right) plus 1 subwoofer. This would not include a center channel speaker at all. Somewhere in the settings of your system you would configure the sound to output in strictly stereo and anything that would have otherwise gone to the center channel in a full surround setup would instead come from the two front speakers (except low frequency stuff sent instead to the subwoofer).  This is sometimes referred to as having a "ghost" or "phantom" center channel if you include surround channels but no center channel.  A 3.1 setup would be 3 front speakers (right, left, & center) plus a this setup it is important that the 3 front speakers match as closely as possible or else you'd be better off with 2.1 instead and running in stereo.  A 5.1 system would include a center and surround channels...most feel that the surround channels matching is far less important than the front 3 matching.  So the first number is the number of speakers around on the same flat plane as you and the screen...the number after the first "." is the number of subwoofers...if there is a second "." and another number, that would indicate "height" speakers; such as those installed in the ceiling to make noise seem to come from above you.

Since this seems to be intended for movies/TV then I think a good subwoofer is an absolute must have, and even better with multiple subs if the room/budget will allow. Some would argue, but I personally think even mediocre surround channels make watching far more enveloping. It's easy to make good stereo speakers create a phantom center, but the only way to make it sound like something is coming up behind you in a suspenseful scene is for a speaker to be behind you playing that sound. If your room allows for surround speakers, I'd spend money on the 75" TV, a Home Theatre Receiver with pre-outs and room correction, a good amp to drive those Thiel speakers (connected via said pre-outs and set up for a phantom center so you don't have to worry about matching), a solid subwoofer, and get a pair of budget friendly surround speakers the receiver can drive so you get that true surround experience...but that's just me.