I'd advise going with a Garand. $500 tops from the CMP. Another $500 into it & it'll be a decent match rifle. But out of the box it should give 3" to 4" groups on the outside, but possibly closer to 2" or perhaps even less. Just depends on the particular rifle. It's reliable to a fault. It's manual of arms is very simple & easy ot learn. Most 6th graders can learn to field strip one in no time. Parts are all over the place & except for something major (like an op rod bending, barrel replacement or receiver issues) you cna make most repairs yourself with the barest minimum of tools. As long as the receiver & barrel are in good shape, you can replace anything yourself. & most problems with the Garand can be solved by replacing an out of spec part with an in-spec part. It's capacity is 8 rounds & it uses a clip instead of a detachable magazine. Most people find this objectionable, but I think they overlook the benefits.
When a Garand is empty the bolt locks back & the empty clip is ejected. You then grab a loaded clip & insert. The bolt releases itself & you're back to shooting.
With a detachable magazine fed rifle when it's empty the bolt locks back. You then have to remove the empty mag. Then you have to insert a loaded mag. Then after you manually release the bolt you can start shooting again.
The Garand feeding system is simpler as far as reloads go. & believe it or not someone who has practiced a bit can keep up with the aimed rate of fire of any detachable magazine fed rifle in a similar caliber.
So I never really saw any disadvantage to the Garand's en bloc clip feeding system.
Now there's a company called Smith Enterprises which used to make mag conversions for .308 & 7.62x51 Garands. He'd modify the floorplate & receiver so it'd accept M14 mags. For the hell of it I asked him if he did the same for '06 Garands. He told me he didn't because there were no available 10 rounds mags in .30-06. I mentioned the B.A.R. mags & he told me that the B.A.R. mags feed in a straight line, while the Garand likes to feed left to right from the mag, so they wouldn't work. However if you have the cash & can talk him or another gunsmith into it you could have them fabricate a .30-06 mag & modify the Garand to accept it. But count on a lot of cash for that project, as designing things from scratch can get pricey.
Another consideration is that untill the AWB expires you'd be forking over a lot of cash to get a gunsmith to increase the garands capacity by 2 rounds.
But by all means if you do that particular project let me know how it turns out & who did the work. I love hearing about uncommon solutions to non-existent problems.
The only real drawbacks a Garand has is commercial hunting ammo, especially 180+ grain bullets could damage the op rod; in a tidal wave or under attack from a firehouse it's possible that the grease will wash away from the underside of the barrel & lock up the op rod; & the damned thing just won't float.
& you can buy adjustable gas systems that will let you use heavier than standard ammo or ammo that uses slower burning powders. But as is stick to mil-surp '06 with bullets from 147 to 178 grains, or handloads with medium burning powders (IMR 4895 & 4064 are great) with the same range of bullet weights.
So if you're dead set on the '06 I'd recommend the Garand.
& speaking of the BM59...
Italy was given a bunch of Garands after WW2. Beretta started fooling around with the design & in 1959 Italy adopted the BM59. Beretta had made Garands for the Italian army but changed a few things in the BM59. Namely they switched to 7.62x51; shortened the barrel & gas system; got rid of the front handguard & shortened the rear handguard; added folding grenade launcher sights that closed the gas system upon opening; made detachable 20 round magazines for it; made it select fire; & made some rather interesting variants. There were about 30+ parts that interchanged between Garand & BM59's, & the rest were either modified Garand parts or newly fabricated parts. They're interesting little rifles. Back in the early 80's I drooled almost daily over The Itali-Alpine model being marketed by Springfield. It was a semi-auto only BM59 in 7.62x51 that had a folding stock & attached bipod. Wish I'd have picked one up. Then again a company is selling BM59 folding stocks & I do believe that it'll work on a Garand with little or no modifications. Might have to check into that further.
In any event the BM59 was a Garand variant & a good one, but it was chambered for 7.62x51 & therefore doesn't meet the '06 requirement. Not to mention it looks like one of those dangerous assault weapons. & while you're in the PRM they're verbotten.
But other choices are kinda slim, mainly cause of the 10 round mag requirement. Aside from the semi-auto B.A.R. or the semi-auto 1917 &/or 1919 Brownings, all the other semi-auto '06's I can think of have less than 10 round mags.
However you cna have the semi-auto B.A.R. trimmed down to around 16 pounds or so. Colt made a B.A.R. for the civilian & police market called the Monitor & it was just a slightly shortened slightly lightened B.A.R. It wouldn't take much to get a gunsmith to hook that up for ya.
& the semi-auto 1917 &/or 1919 has belts, so up to 100 rounds can be loaded & shot without stopping to load fresh belts. As for parts availability that shouldn't be a problem, as the only parts they changed were the trigger/sear/disconnector & the right side plate. All other parts should be interchangable with the standard 1917/1919. If it worries you pick up some spare trigger parts if you buy the thing. Same thing applies to the semi-auto B.A.R. about parts availability.
Both the semi-auto B.A.R. & the 1917/1919 are kinda pricey (for me at least) but between $1500 & $2000 should get you one. I have no direct experience with either but the design isn't overly complex from what I've been told & they should be fairly easy to repair as long as you have the spare parts on hand.
The Saiga AK based '06's do look interesting. The AK system is legendary for reliability. Only thing I'd be curious about is what kind of accuracy it gives, cause AK's aren't known as tack drivers. Still it does look like an interesting idea.
The commercial rifles (Remington 7400 & Browning BAR) have a good reputation from what I've been told (again, no direct experience) & would be good choices for hunting rifles.
But I would recommened the Garand in '06 above all others. I'm biased I admit; but I think a Garand would serve damn near any need you'd have for a rifle.