Neck Turning

So I'm new to reloading (like don't even have a press yet, new) and just compiling all the info I can before putting my bench together. All I have so far is a hand decapper and a wet tumbler. I've been very interested in getting started for several years, but getting much more interested now in today's environment. I have been saving brass (mainly 223) over the last few years and have an assortment of ~3000 pieces of different brands like hornady, remington, PMC, federal, ext.... Most of what I have is PMC because I was always pleased with the results of their Bronze ammo at ~.30/piece, which was also the primary reason I hadn't gotten into reloading until now.

Anyways....My question is about neck turning. I assume it would be very necessary for someone in my case to add something like Hornady's Lock-N-Load neck turning tool to my priority list of things to put on the bench because of the variety of cases that I have. Is that a fair assumption, or am I wrong to assume that the variety of brands makes a big difference in neck case diameter? Since I'm getting into reloading to ensure supply and save some money anyways (I do realize both those very well could be piss dreams these days lol), I'd really want to improve precision too. I was shooting 3/4" groups with the PMCs through my AR, but would really like to get that down to 1/2". I also have a 6.5cm that's currently shooting 1/2" groups with Hornady ELD Match and I'd really like to get it shooting tighter as well. The brass I have for 6.5cm is all Hornady, S&B, Federal and Magtech. All once fired.