You'll be fine with the Lightning. A lot of us here started out with Ugly Stiks, and other "lower-end" rods and caught fish.
You have a limited budget, so stick to it. A lot of us have a habit of feature creep when talking to guys on budget, and that's not a problem per se, just what happens. A $40 dollar rod is fine, but if you only spend $20 more .... and next thing you know you're up to $100 and way over budget. And all of it is guys trying to help you.
Within your budget, there are a number of rods to choose from. Some aren't easily found without shipping, and that may or may not meet your budget. So if you're wanting to buy local and the Lightning is there, get it.
The Shock is the elder brother to the Lightning. Is nice, geared for braided line, etc., but most rods (even the Lightning) can handle braid these days.
Your reel is perfectly fine for drop shotting as well.
If and when you can afford to upgrade to finer gear, then do so. Don't fret now. You'll still catch fish.
You can even use your Ugly Stik, but as others have said, it is heavy (unless it is the Lite version) and not particularly sensitive. Works for some stuff just fine, though.