Howdy, if all you want is to trail wounded deer and not to hunt deer with dogs then my best suggestion would be to ol common but trust-worthy BEAGLE. 1st the dog woll not be allowed off lease in the woods; a beagle is much easier to handle on a leash then say some 80lb hound; remember the wounded deer is likly to head for the thickest cover it can get to and you have to follow it with a dog on a leash. 2nd a beagle eats a lot less then many other hounds thus is cheaper. 3rd remember what the hound is to be used for Blood Trailing and not for hunting so there are limitations to the dogs use. keep it small and slow the last thing you want is a hard pulling, large, fast tracking dog on a blood trail in the middle of the night.
i have trained many dogs and currently use a blood trailing dog to date however mine is a 85lb cur that is used to hunt wild hogs/deer as well as blood trail. And believe me you do not want to have him on the leash on a hot blood trail in the middle of the night he will literally drag you thru the brush.