Look for a post WWII BSA sporterised P14 in 303 Brit. All the work is done, may already come with a flattened 5rds mags box. Feeds, shoots, mostly drilled and tapped for scope rail. win receivers are always the best choice but others, including Eddystone can be just fine too.
At a gunshow in good quality.... around $200.
Can you build what you want, of course. Want to throw upwards of $1000 at this project?
And then all you end up with is a semi custom $250 rifle...
I have played with a bunch of 303 British. Then I moved to the 308 Win and life just got so much simpler.
If you are feeling nostalgic, why not just grab a Mosin Nagant? All the rimmed goodness with great after market trigger, and upcoming accessories. Upfront cost is zip and they can shoot very nicely for an old workhorse.
Jerry