Barry acts very strange for the good reason that you shall find out while playing Resident Evil. Of course the first thing you seem to notice about him is that he’s quite clumsy and does many very stupid things during the game. I think the idea was that he was like this because of the stress he's under, but instead it comes across as it being the way he is and you can't help but laugh at the things he does or says (master of lockpicking comes to mind right now).
Of course you also can’t help but feel that Barry is a great help in certain situations, especially when Jill is in a lot of trouble. You'll find he comes to her rescue very often while exclaiming "What IS this?" and perhaps killing anything that might be a threat to Jill or himself. It's actually something you'll notice often with Barry, his overstatements on things or the repeat usage of 'what is this'. Yet again something I laugh at often during the game.
Being a member of the N.R.A. he cares deeply about his guns and the use of guns, but that care is overshadowed even more for love of his his wife & children which comes first, and the welfare of his fellow teammates secondly. It seems Barry is very much a person to help out his team mates, but as I mentioned earlier it might not be of as much help as it should be.
During the first part of Jill's game (the only scenario he appears in) he'll turn up quite often as you search the mansion for clues. He may even give you a weapon or ammo in order to help you around the mansion. As the game goes on Barry will turn up in vital moments and help you on the quest to finding the answers to what is going on through clues he and items that he finds around the mansion.
You'll never get to play as Barry, but during the game he'll be using a Magnum ("I HAVE this!") and Flame-thrower as weapons. As with most weapons used or seen during the game, details of them can be found in the weapons section here.
Barry has been mentioned in later games, quite often in Resident Evil 3 where he makes an appearance in one of the endings of the game as the pilot of a rescue helicopter.