Decide what kind of rifle grabs your imagination, then consider the chamberings that are available for that particular rifle, rather than limit yourself to just two cartridges. There are no bad cartridges, but some cartridges are impractical for some applications. You might as well consider everything that is readily available. While there are no bad cartridges, there are some pretty crummy rifles out there, so don't let cost alone be your deciding factor.
Things you need to consider are:
your budget, as it relates to whether you should buy new or used,
your previous shooting experience,
what the rifle is for,
under what conditions will the rifle be used,
what type of action do you prefer,
stock material, as it relates to the ease of fitting the rifle to you,
barrel length, as it relates to A) balance B) the ballistic performance of the cartridge,
rifle balance, does it shoulder and point naturally, or do you struggle to find the target, then struggle to stay on target,
can you cycle the action with the piece shouldered or is it too long to reach, is the action too stiff, or is the piece too muzzle heavy to hold while the action is cyucled,
is the trigger manageable, if not is it adjustable, if not are after market triggers available for that rifle,
iron sights, or plain barrel, hint - if the rifle has irons you can start shooting right away if you can't afford both the rifle and a scope,
ease of mounting a scope, hint - if the rifle has to be drilled and tapped for scope mounting, it increases the cost of the rifle,
choice of quick detachable, or permanent scope mounts, hint - QD mounts allow quick for scope changes or switching between glass and irons,
a realistic estimation of how frequently you'll shoot,
cost of ammunition based on how frequently you'll shoot, hint - 20 rounds a week per year = 1040 rounds @ $2/ea = $2080/year
availability of ammunition and/or components if you intend to handload.