For the choice would be how soon you plan on getting into reloading. The .44 has the a substantial edge in factory loads. But handloaded, the Colt can be close to it's equal. Although within it's capabilities, the Colt will get the job done. Handloaded the Colt would be my choice, just cuz well 2 reasons. One being nostalgia, the other and it's silly, I have a peeve for calling something it ain't. It's been that way forever it seems, but why call it a .44 when it's a .429.
Revovlers are great and both Smith's a Rugers are well made. But Bill touched on the TC's, and they are my favorite. I don't consider ultra fast follow-up shots that critical. Part of what I like, is the lack of cylinder gap adding to the noise level. Then too, you sounding budget minded like most, while the TC might cost more in the long run pending on how you get it bought, you can spread the cost out. But the frame and grip first, then shop around for a barrel. Good used ones are often available.
Persoanlly I would have to have some custom work done. Cuz the sweetest close range rig I envision would either the Contender/G2 or Encore with the .45 colt chambered in 9" bull barrel. Although, beings my eye's don't like open sights so well anymore, I would put a holo on it.
But at least doing it this way you can spread the cost out. It's not as hard on a tight budget, which I'm on most of the time.
Dave