There are lots of sets of LOTR, and multiple sets of The Hobbit + LOTR. Usually you end up having to buy the Silmarillion separately. I don't know what all is out there, but I only found this set of all five on Amazon, and it's clearly a display set. I'd buy it if I had an extra 700 dollars lying around, but even I can't justify it under normal conditions.
If you really really want 5 "keeper" books that look good together on the shelf, you can try to find the hardcover volumes I have, though I think you'll pay a good bit more now than I did when they came out. I have The Hobbit illustrated by Alan Lee (Houghton Mifflin); the LOTR box set also illustrated by Alan Lee (also Houghton Mifflin); and the Silmarillion illustrated by Ted Nasmith (Harper Collins). They're not actually a set, but they look like it until you look closely.
But that's just a display set, bought for its beauty. Most of us have at least one "reading set," typically paperbacks, that we're willing to let get dog-eared with re-reading. Since you're just getting into this, I'd start with something like that and wait to buy the big volumes once you know you're in love with it. There are lots of inexpensive options out there; I would say just have some fun browsing through the ton of options available on Amazon, and pick what you like. The text will be the same in all of them, so just choose what fits your style and your budget.
Two things you should stay away from. any Del Ray mass-market paperback sets (poor printing and other issues), and anything authored by David Day. He has some very attractive-looking collections and individual volumes available; the printing is good, but the text is poor. He is a pariah in the fandom for his bad (and inaccurate!) writing, failure to note what is Tolkien's content and what he just made up, and other less-than-honorable behavior. He makes a good living off this fandom, but not respectably. He's also responsible for the infamous "lung map" which is widely acknowledged to be the worst-ever map created in the Tolkien fandom. And maps are important in this fandom!
Which reminds me: you don't need a bunch of books not written by Tolkien, but you do need one: Karen Wynn Fonstad's Atlas of Middle-earth. It's inexpensive and indispensable. You can do fine without it while reading The Hobbit and LOTR, but it'll be a big help when you get to the Silmarillion.
Once you start reading, keep posting here! We love to hear from first-time readers as they make their way through the books. There are no dumb questions, and lots to discover!