Add the 223 Rem to your list... way less components, bullets are SOOOO much better today. 300yds is a chip shot for a modern 223. 22cal stuff is typically easier to find as are mid burn rate powders and SR primers.
Me, I would look at a donor action that can accept prefit match barrels. Factory barrels are so hit/miss these days... but the cost to buy a factory rifle has surged in the last couple of years.
My favorite donor is the Rem 783 (good used basic hunting rifles are around $450/500). The HB versions which can come in 308win or 6.5 CM around $650 - I really like these with the larger bolt handle and heavier profile barrel. Operation can be super smooth and accuracy potential is fantastic (I run these actions in my PRS and ELR rifles). Trigger is also easy to tune to have a very nice pull.
the 783 is going back into production and I suspect more options to be on dealer shelves going forward.
LOTs of new chassis and stock options have popped over the last years. The popular trend is towards chassis with det mags... the PRS game has exploded with lots of supporting bits and parts. I find the MDT XRS to suit all the needs/wants I have in both a target stock as well as a PRS stock (chassis don't fit me well).
there is no reason you can't find a Rem 783 donor, spin on a quality match barrel, drop into an XRS stock and stay in your budget. THIS can shoot with the high dollar custom rifles for a fraction of the costs.
If you want to stay with a 308win, cost per bang is around $3+... missing gets real expensive... match barrels are dirt cheap vs the expected lifespan.
XRS stock, McGowen match barrel in 22 CM, some accessories and bits... easily reach out to 1500yds.
Based off a factory HB version with lam stock. I had the DBM which is not easily available so this would be factory Det mag typically. The factory mags actually work really well and you can single load by dropping a rd on top easily. With a Mcgowen match barrel in 223Rem... is my new varmint rig. Even with lighter bullets... poking to 800yds is easy. This barrel loves 75gr ELDMs and I have pushed this bullet well past 1000yds.
If you are only range shooting, single loading using a LA may make finding a donor easier IF you are ok with the factory stock or something like a Boyds. No support for the 783 LA in general
other actions that are just as easy to set up include Rem 700, Tikka T3, Wby vanguard/Howa 1500. These are factory actions well built and decent aftermarket support.
Savage used to be my fave but over the years, they have come up with so many variations with an unfortunate range of QC, I can no longer recommend them as a brand. If you want to go this route, make sure you can inspect and test the action/rifle you want. If you can pull the firing pin assembly out of the bolt, make sure yours has a full length spring. If you can find an older Stevens 200 or SA of that era, these can be superb donors... but you can no longer go by name and numberings to mean anything anymore. Weak ejection is a common problem that has plagued this action for years. I am not a fan of the Axis if you want a long term build.
Today, finding loading components is the biggest bottle neck. 6.5 and 30cal are SUPER popular so supplies are strained and costs have skyrocketed. The 22cal is also popular but far more available. 6mm is a tough spot due to massive demands from the PRS crowd. I have moved heavily to 22cal as components are far easier to get.
If you are going to reload, start by trying to source primers THEN decide what you can build around that. NOTE, many popular chamberings have both SR and LR brass. A growing number of shooters will have both primer styles so they can shoot their rifle based on what they can find.
Welcome back and I hope you can get set up for your type of shooting. If I can help, pm or email.
Thanks
Jerry
PS - with the popularity of rimfire PRS, we routinely shoot out to 300yds with accuracy. This tech has come a long ways.