FWIW, I recommend not totally cheaping out on the first rod. Don't go crazy either. But if you do get into this sport, there's no reason a first rod can't hold a fairly high rank in your future arsenal.
Action and size is more important than anything. If you generally intend to fish mainly bigger water (as most beginners do), go with something at 8 1/2 or 9 ft, around a 5 wt, that's advertised as medium-fast action.
My first rod was a White River (Bass Pro) brand. It was a fine rod for a beginner that came in right around $100 at the time. That said, it's downfall was that it broke easily. On the first break, I replaced it with the same, which also broke. Many of the cheaper rods do this. I've seen a few Cabelas branded rods too. And not to say they have none that are good, but generally, I didn't think much of them.
That said, some fly fishing specific brands make some pretty good stuff in the same price range. Cortland makes some quality entry level rods, and I have a GRX that is still my go to brookie rod at under $100 new. They don't make that anymore, but I'm guessing the "Pro Cast" model would suit a beginner very well.
TFO is a well known company that makes very fishable gear at a good cost as well. The St. Croix Rio Santo is a good bet from a good company that's gonna come in somewhere between $100 and $150. Redington, Orvis, Loomis, Scott, etc. all offer entry level rods that will suit you just fine. I'd recommend them over taking a chance on a Walmart special or a Cabelas/Bass Pro branded outfit.
i.e. stick with the major players in the fly rod industry and go with one of their entry level models. Spend $100 or a little more.
I'd say you can cheap out on the line and reel, but you already got a pretty high quality reel.