I'm in agreement with Moe on the calibre choice for med. game up to 400m.
3K doesn't leave much for optics after the rifle, mounts, rings, sling so unless you open that budget um about 1k more or hunt hard on the EE your not going to attain your goal. In my experience and within your budget consider restocking an M305. It might be on the heavy side but most of these black rifles are in 308. For that 400m shot on medium game I would forget anything less than 308.
Moe
Below are some/all? the NR Semi.-Auto. Black rifles I know of (in Canada) in the .308 calibre.
Some shoot better then others, but all have the accuracy
potential for hunting med. game up to 400m.
with quality ammo. with perhaps a little tweaking required for some...
FNAR under $1,700+/- new weighs about 9lbs. standard barrel, approx. 10lbs. heavy barrel. (MOA accuracy or better possible, but more complexity in dis/assembly),
Robinson Arms XCR-M $3,200+ new, $2,500+/- used, 9lbs. with light barrel & 10lbs. with heavy barrel. (handles well, simple to break down with good warranty support),
Famae 542 $3,000 reg. new (on sale now $2,650 @ The Shooting Centre) approx. $2,500+/- used & weighs about 8Lbs. (expensive #5 shot magazines and spare parts may be harder to find, saying that The Shooting Centre out of Calgary does care/warranty for all there Famae rifles sold),
ATRS Modern Hunter new $4,000+ used slightly less, as light as 8Lbs. w/o optics. (very well crafted, but cannot feed all ammo. types, possibly MOA or better accuracy and a Canadian manufacturer so no worries with warranty...),
Norinco M-305 new $500 & weighs about 8lbs. w/o optics (affordable, good value and aftermarket stocks are available as are many upgrades to improve accuracy...),
Sprigfield M1A new $2,000+ similar to the M305 (the M305 is copied off of the M1A) & has many options available for improving accuracy just like the M305 does,
Keltec RFB a Bull-Pup style forward ejecting rifle, new $3,000, used $2,500+/- approx. 8lbs. a good choice for hunting in heavy bush due to it's compact size...
It all depends what you really are after. All these rifles are priced approximately and w/o tax, so not all of them are in your price range.
Also you must consider the cost of an optic (plus a case, sling and extra mag.'s etc.), because once the cost of optic is taken into consideration (quality scopes are generally around a $1,000+ new) your choices are even less; especially if buying new.
I personally like the idea of one rifle for all purposes (target shooting & hunting etc.) As it allows for a larger budget then if buying a semi.-auto. for target shooting and a bolt action for hunting, plus you get more experience with the one rifle and that never hurts when it comes time to make that 400m shot.
Many of these rifles can be made to shoot very well and a couple may even get close to quality bolt action accuracy, while others here will be relegated to battle rifle status only (at least w/o a considerable amount of work done and/or funds spent) meaning 2-4MOA. Some would argue that 4MOA is not enough for a 400m shot on as medium sized game and I would agree. So with that said you might want to think about the accuracy potential of each rifle and how much it would cost to get the accuracy you want with said rifle (easier said then done).
The Modern Hunter is very similar to an AR rifle (there are several parts that interchange as it was designed to be similar to an AR) and is sold as a match grade rifle.
The Famae 542 is still in use as a battle rifle in the Chilean Army and would work well for a multi-purpose hunting rifle while the FNAR may be found in a SWAT team role, precision target or hunting rifle.
RFB's and XCR-M's along with the M305's/M1A'a all have there place amongst Canadian shooters and can serve most any role needed, especially after a little tweaking and/or effort with handloads.
I hope this helps a little and that I've covered all the rifles available; do your research and get specific with your wants/needs and complete budget including all accessories and scope.
Although these rifles can get expensive, they do hold decent resale values if taken care of well, so worst case scenario you lose a few hundred (plus taxes

) if you decide you want a different model (and you'll probably want them all

).
Cheers D