1)
You need a either a phono pre-amp, or an old receiver/amplifier with a ‘Phono’ input’ (turnables have a lower output than almost everything else you might plug into a stereo).
Amazon.com has a guide – Learn All About Phono Preamps
2)
You can get powered speakers for the simplest setup: turntable + pre-amp + speakers.
There are tons of choices starting below $50, going to $400 Bose systems and beyond.
Otherwise, it’s: turntable + pre-amp + receiver/amplifier + speakers
Advantages are multiple inputs, a receiver includes FM radio, it’s typically louder.
3)
It looks like you have a cartridge (the part with the needle). But if that needs replacing, this page from garage-a-records.com has a great variety. Below $50 I have had good luck with Audio Technica. Between $50 and $100 I like Grado.
Like any other hobby, learn by trying different things. There is no one best thing, and everybody has different likes/dislikes/opinions/budgets. Don’t be talked into spending more than you want.