I'm sort of surrpised you're having issues with turning the fet on fully; no, it's not a logic level fet, but in the datasheet it shows you can support ~ 50 A with 5V on the gate. Far off from the actual rating of the fet but if it's what you have, it should be able to handle a measly 1 amp load without getting too hot/dropping too much voltage.
How were you driving it before, like, with what circuit? Just a pushbutton, or an arduino, or something else?
Oh, and as far as what to recommend, IRF44 are fairly easy to come by on most websites.
You're really not dealing with much power at all, so honestly, pretty much any logic level fet that can handle over 5 amps (for safety margin) would probably do the trick fine.