The difficulty will depend on what's available in you area and/or easy to get online.
I would look for either a vintage receiver or a newer surround receiver to start you off. If you don't need much power, one of the small Chinese amps, such as Lepai or SMSL, might be enough to start you off on that budget. But you would need a phono preamp if your receiver or turntable doesn't have one built in, so account for that in your budget if necessary.
Speakers, I would recommend a good pair of 90s/00s speakers although vintage speakers might be able to be found as well. Alternatively, ELAC, Pioneer, Infinity, Dayton, and others make highly regarded new entry-level speakers that can be had for a good price.
For turntables, vintage is probably almost exclusively your only option unless you can get your hands on a new ~$100 (in the US at least) Audio Technica, Sony or Pioneer turntable.
Thrift stores, EBay, and other online auction sites are good places to hunt for gear.
Without knowing what's available in your area, it's hard to give specific recommendations. Unfortunately I can only speak from a United States perspective. Once some options start to be revealed, I can probably be more specifically helpful.
