What do you mean when you say "hawken"?
Are you referring to a factory made gun that is almost nothing like a real Hawken but is called that by the marketing department? Or are you considering a fine custom made Hawken replica?
By target shooting do you mean bench rest, chunk gun, buffalo matches or offhand?
For all but offhand, I would reccomend the .50 as it has good wind resistance but mild recoil. It uses less lead and powder than bigger calibers. Recoil can be very tiring, even if not punishing, for an all day competition.
For offhand the .45 and .40 would be a good choice but could make it a bit barrel heavy if the barrel is very long.
In all cases I have mentioned, the 1:48 twist will work just fine. If you are going to longer ranges as for silhouette matches and such the 1:66 will handle heavier charges better.
The .50 is popular these days because it is a comprimise.