>>31651912>whether to make my character DEX or STR basedUnless you're trying for some specific gimmick build, melee characters should default to being Str-focused (with the minimum Dex needed for feat requirements). Your AC may suffer, but not by much, and by mid levels items that give other forms of defense (X/day spell powers, concealment, miss chance, etc) become much more important than AC for actually avoiding getting hit.
>any way to substitute the loss of DEX goodness (especially acrobatics)?Aim at getting Boots of Striding and Springing (+10 foot speed, +5 to Acrobatics) or Feather Step Slippers (ignore all effects of difficult terrain and can take 5-foot steps in difficult terrain). Both are cheap enough for low level characters to get their hands on.
>Any way to bypass armour penalties for acrobatics and maybe climbing?Agile breastplate armor is only a little more expensive than a normal breastplate, and it has only a -1 penalty on climbing and jumping. If you get a mithril agile breastplate, it'll have no penalty to climbing and jumping, and only a -1 to other checks affected by ACP.
>Is Vital Strike worth takingNo. Flat no. Vital Strike is a trap. It pretends to be useful, but whenever you can full attack you'll get more out of full attacking, and in the cases where it would actually be useful (such as in combination with Spring Attack), it's been written and errata'd to specifically make it incompatible with those.
This changes if you're using the Mythic rules, as Mythic Vital Strike multiplies all your bonuses (effectively letting you actually combine multiple attacks) instead of only the weapon damage dice.
>Do I have any chance of achieving this concept, without angering my GM with game-breaking build?Yes. Plain fighters are never game-breaking in Pathfinder.