I went thru what you are doing last year while planning a Safari to Africa. I wanted a 416 Rigby for DG and was shopping for a CRF rifle. The new rifle options are limited. I already had a FN Browning Hi-Power Medallion Grade in 308 for PG that was fantastic. I paid $1250 for this magnificent rifle. While looking, I found a used FN Browning Hi-Power Safari Grade in 375HH. I probably paid a bit much for it at $2450 but it was in great shape and upon inspection appears to have not been shot very much. Just be certain what you are getting as some of the later production guns were push feed design instead of CRF. I think the Brownings are a bit above the Pre-64 Winchesters and might even shoot slightly better as well. Both rifles performed magnificently on Safari. Other advice is do not cut costs on your optics either. I started with a 1.5-4s Leupold but eventually ended up with a Swarovski Z6i.
I often have found that the best used rifles are on auction sites. Poulin, RIA, Invaluable, etc. You will usually pay market price or slightly less but will get better quality in the end. These sites tend to specialize in estate sales where Grandpa has passed on and his grand kids do not want or like guns and choose to sell them all. Unlike some others, hunting rifles, especially those bigger boomers are not often shot that much. So, the bbls are usually in great shape and will last several lifetimes if cared for.
Following my first Safari, I decided that each time I go back, I would acquire and develop a new pair of rifles for the next hunt. Why? Half the fun of the Safari is the planning and preparation leading up to the hunt. I am going back to Africa in 2025, and as such I watched the auctions. Actually, while travelling to the airport to leave for Johannesburg, I bought a lovely CRF custom ER Shaw Enfield P14 rifle in 375HH. It is much more fancy than the plain looking FN and shoots a bit better. I was prepared to pay upwards of $3k for that rifle but got it for $800 plus auctioneer fees and shipping or about $1200 all in. Had I known that it was going to go off so low, I would have also bid on the matched custom in 300HH mag. I was sick to see it sell for $500 (a huge bargain).
After my return, and since I missed out on the 300HH, I was casting about for a good 30-06 or 300WM rifle for use on longer range PG. I found a nearly new looking Husqvarna Swedish Mauser in 30-06. This rifle turns out to shoot better than both my FN's and equipped with a more modern optic than my 308 will be perfect for long range hunting. I am in the process of testing 180g ammo with it now and was uber impressed in the first outing with 2" groups at 300y from the bench and 1/2" groups at 100y. Whatever you choose, be sure to enjoy the ride. Pics below: 1) FN Browning, 2.) The new brace for 2025, ER Shaw P14 Custom 375/Husqvarna, 3.) Close up of the Husky 30-06.