They are a little pricier than the Phoenix Arms, but you might consider Taurus PT22.
Definitely a step or two up in quality over the Phoenix Arms, and actually kind of a cool gun.
Personally, I'd just carry it, but if I was determined to keep it my tackle box, I'd put the gun in the box before I went out, then take it back out when I got home. Otherwise, I'd slather it with heavy oil if I was going to leave it in the box.
In fact, something you might consider is a snubnose .38 - Rock Island .38 snubies are $234 at Bud's Guns.