RE: I need a recomendation on a centerfire
You're asking for a lot, really. The problem is that if you want to meet the bigger game firepower requirement, you're going to get into a power level that, I think, is a bit much for a 50+ round day of plinking/paper punching at the range. The .308 Win is a great choice for anything up to a elk, as is the .30-06, but in a lightweight sporter both get a bit uncomfortable on the shoulder after 20 or so rounds. On the other hand, you can go with an accurate and comfortable all day shooting round like the .243 or .25-06, and while both will certainly get the job done on deer, they are a bit underpowered for elk sized game (which is not to say that either won't do the job, the 25-06 especially).
Personally, my recommendation would be to save and buy two CF rifles. Get yourself a light big game rifle in a suitably powerful cartridge, and then get a varminter/benchrest rifle in a lighter but accurate cartridge like the .22-250 at a later time. But if you can only afford one (and I can sympathize), I'd go with a moderate cartridge like the 7mm-08, 280 Rem, or .270 Win. All should do fine for elk at moderate ranges, they are time tested deer killers, and they won't bruise your shoulder or break your bank account.
That being said, the rifle really depends on your personal preference. If you like a bolt gun, all the major brands make good rifles, differing only minorly in features and asthetics. Savage makes a perfectly functional and sturdy rifle that have a well deserved reputation for good accuracy at an attractive price, the Remington M700 is a very good rifle if you like a two-position safety that doesn't lock the bolt (a bolt-locking safety is a feature that I prefer, again it's personal preferance). I'd also look at the Rem 798, which is a Mauser 98 clone action that Remington imports from eastern Europe. The Rugers M-77 Mk II's are also very good. If you can afford to step up the price, the Browning A-bolt and X-bolt are both very nice rifles.
You also mentioned the Benelli R1, which suggests you are open to a semi-auto. I, personally, don't care for the R1 because I don't like the Eurotrash styling, but I don't doubt it's a decent rifle. My choice and recommendation for a semi-auto would be the Browning BAR Safari, which has the old style steel receiver (vs aluminum for the Long and Short-Trac versions) and furniture. Great, time tested and proven semi-auto, and it looks nice (IMO) too.
Mike