A lot of good points have been made so far...but if you want my personal perspective, it would be this:
I got into hifi in the mid 70s, where Vinyl was the main source, backed up by Cassette Tape, or if you were lucky, Reel to Reel. The importance of the Record deck was seen as paramount, often with half your budget being spent on it. The sound back then was often mellower and easier on the ear...which is why many of us from that era are sensitive to the very clean, often sterile sound of many modern systems....which has us quickly retreating to the safety of Valves, Class A, Vinyl and traditional speaker brands like Harbeth and Spendor.
From us old farts, Vinyl can often be seen through rose-tinted spectacles...where all albums were gloriously musical and wrapped you up in a lovely warm cocoon of euphony.
Newer enthusiasts are fascinated by this intriguing piece of "witchcraft" from yesteryear, where music is somehow produced by lowering a needle onto a spinning vinyl plate, with grooves cut in it....and prior to that, Shellac (a a resin secreted by the female lac bug, on trees in the forests of India and Thailand). Somehow, this has an appeal that goes far beyond the music.
Vinyl is a vocation. This is not about sticking a silver disc in a drawer and pressing play on a remote, or clicking an icon on a computer. It is a ritual fed by tactile and sensual inputs. Record covers are a mini canvas for artwork, out of which slides an inner slieve, that protects the treasure inside. This treasure needs nurtured and when put on the Platter, changed after about 20 minutes, to Side 2.
As Mark said above, this is a rabbit hole that runs deep. You find yourself in a whole new world of Deck designs, Arms, Cartridges (Moving Coil/Magnet), phono stages, alignment, tracking angles, tracking weight, anti-skate, feedback, earthing, static, Vinyl quality. Whether you see this as unmitigated torture, or magnificent hobby, is down to the individual. If you are a hands on tweaker, you'll love it; if not, you may find the whole thing gives you a migraine. So my advice is know what you are getting into and (as has been said), work with a dealer that knows his way around a Vinyl set up.
I agree with DDC, that to do Vinyl justice, you need to be prepared to spend more money on it, than you would a budget Digital Source. Back in the day, I went from a Trio KD1033B -> Rega 2 -> Rega 3 -> LP12/Asak/Ittok.
I loved the sound....but it's worth remembering, that there were also differing qualities of Vinyl / Mastering....and it could sound nasty, so this is not an automatic route to audiophile Valhalla....but done right, can be very rewarding.....and the albums that came out pre CD almost always sound better in their original Vinyl form.
I didn't like the sound of early CDPs and only changed when Linn brought out their Karik/Numerik....which was the only analogue sounding one I'd heard.
I also think, that assuming Digital can't sound musical and engaging, is simply wrong. If an album is well recorded....and Linn Records show how well this can be done....the result can be very natural, dynamic and life-like. The problem is that music for popular appeal is very poorly recorded, so it will sound loud on an iphone with cheap headphones.
I don't miss the faff of a TT (but I got it out of my system....so to speak). By carefully selecting my system based on components that deliver the soul and texture of the music before all else, I am listening to the best sounds of my life.
So to sum up, if like Neo from The Matrix, you want to take the Red Pill and see how deep the rabbit hole goes, then:
- Be prepared to spend...both on the TT and building up a record collection from scratch
- Understand that this is not a "plug n' play" solution. For instance, if you have an old wooden floor, just walking around can make the needle jump.
- Realize the sound you will get will be different, but not necessarily better.
- Be aware, that back in the day, there were many more sealed speakers, which cope with the rumble from a warped record better.
Anyway, I've waffled on enough and hopefully have given a little insight that might be helpful.