Hi,
I wouldn't want say so much about the other stuff as yet, but Raul's advise to stick with the V15 III gets my full support.
You have not mentioned your current stylus type (see in front of the protection flap) or its condition. In fact I would expect its condition may be still in good order.
I use a V15 type III right now and it runs with the (upgrade of old) stylus VN35MR.
It sounds VERY nice, B U T only after using the correct VTA setting i.e. about 1-1.5mm arm down at the pivot! Otherwise at level arm it usually sounds too bright and un-musical.
I use this old V15 in my SME-10 TT and SME-V arm a ~ $15 000 rig and it's a good match. Sounds better than some $3000 plus MC cart!
This brings about all this other analog stuff like Zenith, Overhang, Azimuth, settings etc.
I would expect, you not having been at it for some time, it may be somewhat of an 'un-known' to you.
IT IS VERY IMPORTANT to have a basic grasp on this stuff. The last time you played records, not much VTA adjustment was practiced (never mind known!) I include myself here in the 70s and early 80s, and then only to be followed by CDs, amen.
I also think your TT will be more than fine to get going, given the correct set-up!
The phono-interconnects as mentioned by Raul are as well VERY worthwhile to consider as they are **usually** not of the best dating from that period.
Your next step, and again mentioned by Raul is the SAS stylus replacement for that V15. But I suggest only, if the current one is worn or not at least an elliptical (E) or hemi (HE) or micro-ridge (MR). Check for the end letters of the VN35xx stylus on your V15 type III. (Displayed on the stylus protection flap ).
Best of luck,
Axel