Let's say you're putting together a HR hitting team and you've got a park picked out that you're building to in order to help them out. Assuming cap isn't a problem, do you try to stack your lineup 1-9 with HR hitters, or do you throw in a few high average hitters for road games, where you may not be able to pile up the HRs?

Basically, I'm wondering if, when people tailor a team to a ballpark, if they tailor everyone to that ballpark and take their chances on the road, or if they try to account for games in other parks that may not feed their strengths.

Depends on if the salary cap is high enough to afford a home lineup/away lineup.  It's easy to do at $255M, not so much the lower you go.

Assuming that you can afford 9 good starters, to be used both on the road and at home

Then the only stat I wouldn't try to build a full lineup around would be HR because it's the stat that can be suppressed the easiest by an opponent's stadium/pitchers.  Unless you are in a progressive or anti-deadball theme where HR will still matter, then I'd work in some more versatile hitters around the HR hitters. 

I've never had success building all-contact teams and will almost always try to get middle-of-the-order power at a minimum.