USGI
Although they had some issues early on...and actually halted production in order to get it sorted out...from early '44 until the end of production in 1945, Remington Rand was producing a pistol that was fully equal to Colt, and some authorities consider them to be superior to the Colt and the Union Switch...and they were delivering pistols at less cost than either contractor.
My own experience with USGI pistols, most of which is with Rand and Colt, since both are more plentiful than the others...tends to make me agree with that. Remington Rands produced from about March, 1944 until late August of 1945 were consistently excellent.
Now for the bad news...
Original Remington Rands are getting more scarce by the day. You can find rearsenaled pistols that vary from very good, all the way to near junk. Many others are mismatched with Colt or Ithaca frames and Rand slides or vice-versa. I've seen many "Original" Union Switch and Signal pistols that had US&S slides on Colt, Rand, or Ithaca frames. Unscrupulous people lurk in the corners of gun shows all over the place. Some don't actually realize that they have an Ithaca-Rand, or a Union Switch and Colt...but the biggest majority do, and they hope to prey on the ignorance of the public.
Because a pistol is a mixed gun, doesn't necessarily mean that they're gun-show cobble jobs. They often got that way in various armories and arsenals when they went in for service...but many are parts guns that have been thrown together from all sorts of Who-Hit-John parts bins...some of which were rejects...by individuals who should leave mechanical things alone. Caveat Emptor applies in full force. If the mixed and matched pistol was correctly assembled...with all gauges used to insure correct fit and function...most of'em are as good as the real deal, although they're not worth nearly as much as a collectible. These pistols are your shooters, and even then, it's best to keep the round count fairly low.
Decent, original and/or correct Rands...Colts...and even Ithacas...are far too valuable to use as common range beaters. Shooting a Union Switch more than a magazine or two a year is sure to send a collector/historian to the coronary unit...although I've shot mine a bit. Shooting a few rounds occasionally is one thing, but to shoot'em hot and heavy is another matter.
On the other hand...you can still find a well-worn Colt or Rand...or a mix-matched pistol...that you can pick up for not much cash and rebuild and refit, and use for a shooter. These typically run anywhere from as low as 350 dollars to about 800, depending on how rough they are. Check the slide for signs of damage at the rear lug faces. Look closely for cracks in sharp corners. Barrels at the front lug faces and cracks on the lower lug at the rear where it joins the barrel. Cracks through link holes in the bottom lug, etc.
Good luck in your search. A USGI pistol...especially a good Colt...just has a different "feel" than any of the modern offerings. It's hard to explain and hard to understand until you put one in your hand.