Interesting question, I either take the singles hitter or the home run hitter.
Anything a hitter can do to not create one of the 27 outs his team gets over the course of a game keeps his team in the game and gives them a chance to continue to score runs. From that perspective a singles hitter who never makes an out will continue to put his team in a position to continue to score runs. Doesn't matter if he's getting a single or walking. How productive his 1.000 batting average is in terms of runs produced is dependent on the other players on the team. For the purpose of this discussion I will make the presumption that this hitter is not keeping up his 1.000 BA via sacrifice hits, which although they can be called "productive outs" are still outs.
On the other hand, a .250 hitter with all HR's has the potential to produce a lot of runs over the course of a season. The rub is that at a certain point the league should start to walk him to avoid the chance of a HR. Let's say you have a player who hits 5 HR's in his first 20 plate appearances without any walks/sacrifices/etc. Not a big deal, he's still going to be pitched to. But let's say you have a player with 25 HR's in his first 100 plate appearances, again without any walks/sacrifices/etc to make the argument more straight-forward. That means he has produced at least 25 runs for his team in 100 plate appearances. Or let's go to 50 HR's in 200 plate appearances (i.e. 2 months of games) Extrapolate that out and you're talking a minimum of 175 runs produced over a typical season (estimating 700 plate appearances for an everyday player). That would be huge, so the obvious change is to walk him every at bat. He still ends up with a .250 batting average but the damage related to 4-5 walks per game might be less (no guaranteed runs) than the damage of 1 HR per game (at least 1 guaranteed run).
The doubles and triples hitters, I don't see where either of those options has the same impact. Neither gives you guaranteed runs like the HR hitter does, and both create outs unlike the singles hitter.
If I am pushed to choose, I'm going with the singles hitter, and I'm batting him 2nd or 3rd. Knowing that he's going to get a hit or walk every time up, I like the idea that if anyone gets on in front of him that he moves those players along or drives them in. My first instinct is to bat him leadoff to get him the maximum number of plate appearances, but since he does the same thing every time I like him in the 2 or 3 slot. Even if the league starts walking him every time that means he's pushing other players who are on base along and giving the 3-4-5 hitters more runners in scoring position.