I too would recommend a rather basic build if you are new to the game. Sure, there are lots of little things that can be done that will, at least in theory, make your character more powerful. The problem with that though is those things are often a matter of combining lots of abilities/feats/items/etc. to stack up to some pretty cool stuff. In and of itself, that's not a huge deal. However, remembering to include everything is. I've been playing RPGs for over 15 years and I still forget things like my Dragon Style chain of feats cause a creature to be shaken when I crit, etc.
As for beating the Half Orc at level 20, pretty much what Dafydd said. The problem here is that at level 20, the half orc barbarian will be far more than just a run of the mill half orc barbarian. There will be magic items, feats, etc. that will all interact to make him more powerful than you might think. Thing is, we don't know what those things are. Sure, the general rule of barbarians is "Smash Enemy", but if he has managed to get to level 20, he'll likely have a few tricks up his sleeve. Best advice is to try to find ways to observe him or learn more about him and his resources as you level up. Things like Scrying can help with this, but there are a multitude of other means as well.
Most importantly, have fun. At the end of the day, as long as you are having fun, then you are doing it right.