In support of what Sevens recommendation, you can get a brand new Ruger MK IV 22/45 with a 5.5" bull barrel for about $360 these days. It has a 1911 type grip frame (and can accept most 1911 grips) . Based on my ownership experience of 4 1911's in .22 and a good dozen Ruger MK I/II/III/IV pistols, I'd argue that the MK IV series is that it is way more accurate, reliable and verisitle than most inexpensive 1911 .22's /.22 conversion kits. ( My Ruger's shoot right up there with my Marvel and Nelson Custom 1911 conversions.)
As an additional benefit, it comes drilled and tapped so you can add a red dot for competition (or just plain fun.) MK III 22/45's (used) should run you about $100 less if money is an issue.

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Dave