First of all as others have alluded, what is your budget either for total or how much potentially a year if you were looking to do it in steps.
If the latter is your route, as below its obviously going to be important for you to take steps that are immediately benefitting without the upgrade just being the limiting factor a few steps later. I note in saying that you will have seen here you can 'always' find something extra to change. But what you want is to not feel the need to go around the loop again within what you were happy to spend overall. If you find that hooks you into listening to more and more, then perhaps a second loop is worthwhile.
Having got my system to a point where several of my personal TT System components were used at the UK HiFi show and there was little at the show to touch it. I have spent much of my 'available tinkering time' in the last year assisting friends and family to get a 'good proportion' of what mine can do for a cost effective price. So I would give some suggestions for which parts to change based on that work that would fit in that budget, with "if you wanted to continue after, the next thing would be".
A question to start. Does the Project T have something like an Ortofon 2M Red or the "Project Pickit" cartridge / stylus? As that can have some influence on some early options. If not which stylus is it.