Unless you haul or pull a fair amount of weight on a regular basis, you really don't need an LT tire. An Lt tire will stiffen your ride a little, possibly cost you a little fuel economy, and they are pretty expensive compared to tires with lower load ranges.
I would advise you to do thorough research about the stock Wrangler HPs before even considering going back with them. All you are likely to find is bad reviews. Everyone hates them, lol. Based on your location and the type of driving you do I would second the recommendation of the Cooper Discoverer H/T Plus. I read a ton of positive reviews on them before putting them on my truck about a month ago. They are still new obviously but I love them. So smooth and quiet! Not to mention they are made in the USA and are priced great. Discount Tire Direct doesn't show them online but if you call them, they can special order them. Took me about 8 days to receive them I think and I paid $163/tire with free shipping. That was the cheapest I could find them. Also, the Discoverer is an XL rated tire which means it's slightly higher load rated than a standard load tire (which I believe the Wranglers are). Here's the thread a did when I put the Discoverer's on my truck.
Oh and to answer your question...it's not going to hurt anything if you buy three new tires of a different brand to run with the new Wrangler that you have as long as you can put up with the visual and mental reminders of having one oddball tire. It may very well wear differently than the other three tires simply because it's a different tire with different characteristics but that's about it. My recommendation would be to shop around for the best deal on a new set of four and then hock that new Wrangler for whatever you can get out of it...probably $25-75 if you are lucky. You might even be able to trade it in if you end up buying your new tires at a place local to you.