Likewise am also left handed. My advice, which was given to me was find a good left handed rifle and don't worry too much about the calibre, which in left handed is somewhat limited. I have a Heym SR20 in left hand in .243. Calibre is a bit small perhaps and ideally I would like a 7mm, but it has three position safety - fully locked, safe on but you can open the bolt or fire. No longer made, but you can occasionally find them - one was sold recently at the Holts auction - 7x57 for £700, with Svarovski scope.
Am seriously thinking about rebarralling to 7x64 or getting another rifle in this calibre to use both here and overseas.
Sako Mod 75 is very nice and available in .243, .270 and 30-06 in left hand - has a separate button to press to unload which is a bit fiddly. Have used the right handed version in both wooden and stainless and good solid and accurate rifle. Sako 85 is not going to be available in left hand according to Gunmark people when I spoke to them at the Game fair.
Tikka's you can't go wrong with. Good solid rifle, albeit the older 595 is perhaps a nicer rifle than the T3.
The Ruger Mod 77 has a good three position safety and available left handed. Friend has one in mountain rifle and knocks over deer very well.
Remington Mod 70 - have used has a two stage safety that allows the bolt to open even with the bolt applied. The annoying thing is that the bolt often catches on clothing when slung and opens itself and then fills up with snow and other c..... But solid action and anybody can and will customise it.
Don't think the modern Mannlicher is available left handed, but then Model M definately is and is a very nice rifle, if you can find one.
Mauser M03 is available left handed - and in just about any calibre you care to wish. Has a good safety system, in that with safety on, striker is lowered sp it cannot fire. You just push safety across to fire, or pull it the other way to unload. Have had a look at a right handed and looks very nice. Only issue is that it has a dedicated detacheable scope mount that looks a little fragile, but am sure it is strong enough.
Don't discount the single shot rifle - Ruger No1 is a nice rifle, likewise many continental rifles. Slightly slower to reload perhaps, You generally only need the one shot, unless you are culling, but have never had an issue stuffing two cartridges into the shotgun as the one skeen of geese have flown overhead and have missed with both barrels.
Have fun looking and don't rush in to the first rifle you see.
More importantly get some good optics - you won't go wrong with Schmidt and Bender 6x42 Hungarian.
Heym SR20