Frank
Can't comment on the Hawke, but if you're only going to have one rifle I'd certainly endorse the .308. It's the only calibre I use, on everything from muntjac and roe up to red......so it's not like I'm biased
I use the same round (150gr Nosler BT over 43.5 gr of V140) for all my stalking. I could go lighter on the muntjac and roe if I wanted, but the carcase damage is minimal so I like to keep things simple.
It's not a harsh round to fire - more kick than the .243 for sure, but nothing like as hard as the .270 IMHO.
You'll find a whole stream of threads on "the best calibre" here on the Directory - it's a bit like poking a hornet's nest with a pointy stick
My two-penn'th is that if you want one rifle that will cope with anything it seems to boil down to .25-06, .270, 6.5x55, .303, .308, 30-06.
The reality of course is that, regardless of calibre, it's more about hitting the right animal in the right place! If you do, it will fall down.
One consideration is that if you intend to shoot abroad there are some countries where you're not allowed to have rifles of a 'military' calibre. But that could just be an excuse for buying another rifle
willie_gunn