At your price range I'd suggest you get an integrated stereo amp with a phono input.
There are three types/stages of amplification involved (in a greatly simplified way, from my fairly simple understanding of the process):
– A power amp simply does the job of amplifying of the signal to a level which will drive loudspeakers.
– A pre-amp does all the tweaking of the signal needed to get it ready for the power boost of a power amp (including selecting the source, volume control, graphic equalisation, etc).
– A phono stage boosts the very weak signal from a turntable to 'line' level (the level of CDs, cassette decks and other sources) and applies the inverse RIAA curve to restore the various frequencies in the signal to their proper levels (more on what's all about in the link) so that a pre-amp can deal with the signal properly.
An integrated stereo amp with a phono input will do all of these jobs in one box. Unless you're getting far more expensive equipment, I don't think there would be any benefit to you in buying separate components.
However, I'm one of the non-experts on this forum, so if someone else contradicts what I say, it's quite likely that you should follow their advice!