People shoot both .44 mag and .44 Special. I shoot .44 Special for rifle and .44 Russian in pistols. The .44's are straight walled cartridges (except for the .44-40/.44WCF, a completely different cartridge) and is easier to load and longer lasting than the necked cartridges but will not serve you as well if you want to shoot black powder.
There are more gun choices in .45LC for both pistols and rifle and the rifles in .45 maybe a little easier to find and cheaper. Handle and shoot as many of the choices as you can before buying. And if you plan to be competitive then you will have to have some slicking and smoothing done to any of your guns--usually the club that you shoot with will have a favorite local gunsmith. Find one that has worked on your type of gun and check out, handle, and if possible shoot a sample his work and ask about prices. There are a dozen or more excellent gunsmiths around the US that are known and discussed on the SASS wire but plan to add about $75 for two way shipping and the time to do it if you don't find anyone local.
For the first shoot or two just come watch. Buy leather and a gun or two and you should be able to borrow a gun or two from people at your local club--at least for the first couple of matches. I recommend that you don't buy "get by" leather or hardware. If you buy the wrong stuff (unless it is quality stuff, just not right for you) at the beginning you may be stuck with it after you buy the right stuff six months later.
Don't be hesitant about cornering the top shooters at the closest clubs and asking their opinions of leather and hardware--they have all been thru it and almost to a man or woman, are among the nicest people in the club and will be glad to help you.
Good luck,
Sky
Sky Marshal, SASS #26,104L