How to accurize (sp?) a model 1911

I have a Colt Military 1911 from years back. I would like to know of the first simple things that might be done to get it to group better. I might replace this gun as a concealed weapon merely since it is far superior to a Sig 228 in 9mm that I carry for "stopping the bad guy". From my far back military days using the M1 garand in National Match Competition (1956-1960) there were several parts that would be exchanged, and of course glass bedding. This was prior to guns built up by the Marksman Unit at Ft Benning. In short, what can I do, or purchase, for my 1911 45 cal to get a tighter group? Are their gunsmiths that specialize in doing this and leaving the gun as much original as possible; and what generally is the cost?

Would appreciate a direct e-mail to me for suggestions: wilbur006@dishmail.net