There is a bit of a shortage of information from the OP on where will he be typically hunting...? And what is he hunting...? If we knew if it's a deer/ elk/ moose gun it would be easier to help out as caliber could be a consideration.
Generally some manufacturers add a bit of an up-charge for a left hand rifle. I don't think that in this day and age of computer software programs that this should be an issue. There may be some minor factors for tooling - but for whatever reasons it's a bias that can turn younger shooters - to - be hunters off.
A lot of companies that could produce more variety - because they have already tooled-up for left hand shooters - need to expand some of their models to get greater sales. Perfect example is Savage Rimfire rifles - made in Lakefield, ON. In left hand they make a standard barrel and wooden stock and have not extended the courtesy to have pictures up on there site and this has the effect of being disturbing to a potential Left hand buyer who is considering a Savage.
If anyone from Savage is reading this post - please do the right thing and have pictures loaded up on the internet site for all your Left hand rifle. This has been ignored for years and is a real turn-off. I interpret this as a marketing disgrace that juxtaposes the company's overall sales objectives.
Savage - best overall hunting rifle IMO 16/116 Weather warrior, M-10, M11/111. Axis, 14 American.
Remington - The nicest rifle they made in Left hand was the Stainless / Laminate stock (with raised cheek rest) but was mostly limited to 7 RUM, 300 RUM and 338 RUM. It would have done better in 300 WM, 7mRM, 30-06, 270, 25-06, 308, 7M08, 260 Rem, and 243Win. They made a Special Purpose 700 in a police design, BDL and CDL.
Armalite AR-50BMG Left-Hand Single Shot Bolt Action Sniper Rifle 50A1BL, 50 BMG, 31 in, Black Stock, Black Finish
Those are a few to start search for and there are a few more brands from Europe and a couple I didn't add.
Winchester - made the M70 for several years before the Conneticut. They made the 375, 338Win., 300WM, 7mRM. In short action they made the WSM and possibly the WSSM cartridges.
Tikka - decent variety - probably better then most companies.
Sako - AV, M-75, and M-85 hunter. Great guns if someone wants to buy one great gun and keep it.
Forbes Rifles - M 24B, M20B.
Weatherby - Weatherby Mark V in magnum cartridges.
CZ - Some Rimfires 552 and 527, in 204 and 223
Ruger - M-77 Hawkeye Standard type Walnut blued barrel, they did make a stainless / laminate, Gunsite Scout, Safari, they have recently announced the release of the American in Left Hand
Browning - A-bolt in Micro Hunter, Hunter, Medallion, Stainless Stalker, X Bolt Hunter, Medallion. White Gold (no longer produced) BAR