I'll give you a slightly different view to think on. (First, I should say I agree with what Benuser and BDL have said, and I've asked them enough questions to trust their judgment.)
The difference is, we don't have to write off your existing knives yet. Yes, sharpening by hand is a great skill to learn. Yes, you'll want to do that with a good knife that you buy. In my own experience, that came with hours upon hours of reading as much as I could and watching videos, and getting over being scared that, the first time I put nice knife to stone, I was going to fundamentally CHANGE it. (Any mistakes can be fixed. It'll turn out well.)
I would consider at least having the current knives that you use the most taken out to a professional sharpener local to you and having a serviceably sharp edge put on them. That will at least buy you some time to get into this brave new world without suffering through dangerously dull knives. Doesn't have to be a master sharpener - in your words, these are the "cheap knives from the bridal shower" - but taking them to get sharpened will help.
I say that in part because picking "the" knife to get is a tricky and ultimately personal thing. As you're now getting started cooking, you might not know yet what you really want from a knife yet, and it's not trivial money we're talking about in this thread. Instead of choosing a basic set of three or four knives at once, maybe pick a knife in your current set that you use and want to replace, decide what you do and don't like about it, and start from there. (BDL alluded to this, but whether you're interested in learning sharpening with a stone, prefer to find a great sharpener to take the knife to regularly, or just don't put the effort into keeping up with the knife will influence the knife you pick, too.)
My story, for what it's worth - I bought a knife set (Chicago Cutlery, with the wood handles - same as what my parents had that I grew up with) when I graduated college. That worked well enough for what I needed at the time. My first "better" knife was a Henckels Four Star 8" chef's knife - I was overseas, my knives were at home in the States, and I needed something to cook with - which I still have and use today. I thought it was everything I wanted in a chef's knife. I now know the handle is too big, the blade is too short, and it has too much curve/rocking for my taste - but it's sentimental, and I practice stone sharpening with it, and it's perfectly usable today.
I've since purchased a variety of other knives that make up my kit today, both Japanese and French, both stainless and carbon steel. Doing it this way - one by one - let me evolve what I wanted in a knife as I became a better home cook. And now every knife in the roll also has a story to go along with it.
My two cents,