This might not be what you are after, but If your intending to make a frame from rough timber that's not profiled..
I will suggest some tools which I would think necessary for the job at hand.
The tablesaw will defiantly be too dusty for you I think.
If your not intending to make a lot of mitred frames, you could get by with planing them instead
on a mitred shooting board.
https://youtu.be/eqWbgkl_ryM
You need a good bench and good lighting sorted.
A hand plane or two is the first thing I would be looking for, incase you don't have any yet.
You would be have to be pretty lucky to get good mitres without having flat stock to begin with.
Search on the bay or for a few Stanley Bailey/Record's or the likes of tooltique. (type this to into ukworkshop search engine and you will find other sellers)
Not much wrong with rusty ones.
I would get some Ultex hones on half price annual sale, or the cheap ebay DMD ones for 3 or 4 quid each.
I have amassed a nice selection of long stainless steel rulers from Homebase for less than a tenner each. (bout the only thing not a rip off in there)
I would get a nice square like this cheap one for a tenner
https://www.axminster.co.uk/axminster-w ... es-ax23310
These are pretty nice Japanese mitre squares in there for little money, at something over a tenner,
which I definitely would buy also.
https://www.axminster.co.uk/japanese-mi ... are-510015
A marking gauge would be nice, the cheapest wheel type marking gauges are 30 quid
and I will be shot for even mentioning it
There's not much more you would need to do a few
You could get by with a fine cutting hand saw like the Bahco laminator if you scribe lines
to avoid breakout beforehand.
I have used on of those mitre saws freehand for a good while, it has server me well, very easy saw to use.
Those might be cheap without the box, and they have replaceable blades, and you could make your own mitre box.
I'll leave out the complicated parts like the groove and the glazing for others to comment on.
You might find it a challenge to get the groove cut... "should" you choose to cut one for the glass.
You could laminate some strips if in a pinch.
A good few variants of planes would be able to do that job, should you stumble across an ebay listing for a cheap shoulder plane or combination plane or other tool that can do the job instead of the TS
Good luck
Tom