If you are indeed playing roto style scoring, then the players eligible to accrue stats are the ones you insert into your starting lineup for any given day. In other words, not the players in slots marked BN (bench) on your Yahoo team page. So yeah, the utility guys score.
Something to keep in mind, and which you are probably already aware of, is the games limit in effect for each position for hitters, and the innings pitched restriction for your pitchers (your league settings should show you both). If the games limit is 162 games at SS, for example, that means you can only score 162 total players games at SS and can't exceed that number by subbing guys in and out. In order to amximize your scoring the general idea is to try and use all of those 162 games at each postion. There will be a running count of games remaining at each postion listed on the bottom of your team page, so keep an eye on it. What a lot of guys do is try to run at, or slightly ahead of the GL so that they're not scrambling to make up games at the end of the season. For your pitchers there may be a cap on total innings pitched - that counts all your pitchers, starters and closers. If your league has an IP max then you should keep an eye on that as well. Again, the idea is to use all those innings, or as close to it as you can come.
From what you've got listed for players there I have a suspicion that your starting pitching needs a boost. I'd recommend taking a look at some different rankings for SPs to see if there's some decent talent available on your waiver wire. Feel free to post your entire roster for more specific feedback (although you may want to do that in the roster analysis sub-forum).
Anyway, good luck in your first fantasy season.