@ddonicht, lots of good guidance here from the vinyl community!
There's lots to know about the proper care & feeding of LPs and vinyl playback, not the least of which is proper storage, good quality anti-static poly sleeves, etc. I hesitated a bit before chiming in with my two cents, which is probably an amalgam of many things already mentioned. However, as a self-described nerd who tends to research things before pulling the trigger, when you have time enough to devote to this, have a read of Neil Antin's "Precision Aqueous Cleaning of Vinyl Records - 2nd edition". Not an easy or quick read, by any stretch of the imagination! However, certainly worth the time and gray cell investment!
Should you clean records before play, even new ones? Absolutely! Does this need to be done before every play? Of course not! However, there are some vinyl afficionados who do. More power to 'em! Is ultrasonic LP cleaning the way to go? I'm convinced, as are many other audiophiles. If the budget can bear it, have a look at the Degritter machine, which is all the rage now. On the other hand, if sticker shock is a factor, you might want to check out "Cleaner Vinyl Ultrasonic Record Cleaning". A bit more labor-intensive and less convenient than Degritter, but a fraction of the cost. Convenience, eloquence and innovation has its price. By all means, though, I strongly encourage you to invest in some sort of record cleaning system or device(s), especially if you are going to get involved with used records! Your ears will be happy you did! Depending upon what the budget will bear, you should have a look at the vacuum cleaning machines or something as relatively inexpensive as a Spin-Clean or Knosti Disco-Antistat. Personally, I would go with the Knosti because of the cleaning brushes, as opposed to the Spin-Clean's pads. In any event, pay particular attention to the types of cleaning fluids employed (you don't need to use what comes with the machine) and, if needed, use only high-quality microfiber cleaning or drying cloths. You can also clean records manually. However, a machine makes this considerably easier. With a properly cleaned record, good TT & cart and good sound system, surface noise is virtually eradicated. You'll be amazed at the deep, dark, black background noise floor the music will be coming from and the dynamic response or, as Messieurs Simon and Garfunkel would put it, "The Sound of Silence".
Another thing I consider indispensable is a good record clamp, like a Michell Reflex. Here, also, you'll be amazed at the sonic improvements this makes. You can also use a record puck or weight. However, I don't see the sense in placing extra weight on the TT bearings or additional mass on the platter, even if the manufacturer says the TT was designed and engineered to accommodate this. If you do go with a clamp, make sure you get one that accommodates the length of the TT spindle.
I'm not sure the Audio Technica - AT6006R Safety Raiser would work with the Pro-ject TT you have in mind. However, if it does, one of these gizmos certainly beats the hell out of having to be ever vigilant so as to prevent your stylus from running into the label at the end of a record. Not a good thing!
Here's another inexpensive gizmo to have a look at: StylusTimer
Helps you keep track of the mileage on the cart & stylus. Not absolutely necessary, of course, but convenient.
Some sort of stylus cleaner is also an absolute must. I would recommend you check in with your cart manufacturer on this to see what they recommend.
Oh! MoFi & Music Direct are an excellent source for new records, There are a few others but you can't go wrong with MoFi & Music Direct.
Welcome back to vinyl and happy spinning!