Vinyl LP's are a passion and an investment. Don't play them on a poorly constructed machine that is designed to destroy the grooves in a few plays.
There are cheap players that look cool, retro and affordable, but in the end they will
cost you more with the destruction of your collection.
Here are some links to affordable options and some more expensive options, but nothing that will break the bank. The most important thing in buying a turntable is to get one with fixed or adjustable counter weight and fixed or adjustable anti skating. The counter weight will keep the stylus from grinding the grooves away and the anti skating will keep the stylus from tearing through the grooves as the record is played. Protect your investment in vinyl for years to come with a proper turntable. The other components can wait.
This combination is just around $200 for a fine player and descent speakers. You can use the turntable with an existing receiver, amplifier, "Boombox" style speaker or most any audio source with a input for just around $99 - AT LP60 only.
This combination is a bit pricer, but will allow for future upgrades as you grow and learn more about the vinyl world. This will be in the $800 range for a fantastic, flexible, lovely sounding system. Again, you can use the AT LP120 with any existing audio source with an input and purchase the rest later.