Try a Pro-Ject Debut III, $400 including a pretty decent Ortofon OM5 cartridge. I bought one last year to listen to Christmas records in the living room, but when I brought it downstairs to compare to my much more expensive 'tables I was astonished. Analog (including this cheap machine) gives you the air that is missing from cd. It's free of the digital haze that restricts dynamics and sense of real space. I'm not a digital hater: my cd player is an Esoteric X-03se, and I love it for what it does. It's just that analog, even the inexpensive Pro-Ject, can make music come alive in a way that cd can't.
But as someone entirely new to analog you may find that surface noise, ticks and pops can get in the way of your musical experience. I never hear them myself, and many of my records are real "beaters" filled with noise. Of course I bought my first record player in 1956, and like most of us who started with analog, there's no adjustment to make. I have a friend who's a very sophisticated listener and knowledgeable audiophile who cannot abide the surface noise. Really the only way for you to find out is to make the commitment, give it two or three months, and resell if it's not your cup of tea. Even if you buy new for $400 and resell for $300 (typical for the Pro-ject) you're only out $100 to learn.
You will need a phono preamp, too. Many adequate ones available for under $100. Or, if you want to push it up a bit, $250-300 for a used Lehmann Black Cube will give you real high-end quality, and it's instantly re-sellable if you give up on analog.
That's all I got. Have fun!
Dan