Good stuff from Neil.
It used to be when I was young (500 years ago) a cheap guitar was cheap for a reason..ie,because it was crap. In the brave new world of mass production and cnc machines quality control is better by a mile.
You can buy Chinese/Indonesian/Korean built guitars now which are capable of being used on a paying gig.
Ask me how I know.
You see this boyo in the pic below? You can buy him used for £100ish quid. Some folk are sniffy about the Squier logo and some don't buy for political reasons. There are plenty to choose from. If you are wondering what it sounds like,I used it on this song.
https://soundcloud.com/skub1955/rock-a-hard-placemix-2One of the areas that makes the difference between you enjoying playing a guitar and finding it hard work is 'set up'. This includes accurate intonation,action (string height from the fretboard) a correctly cut nut (rare on almost everything regardless of cost) and for sound,pickup height.
All that stuff may seem overkill for the question you asked,but I'd always advise playing a guitar before you buy and if you are unsure,take along a friend in the know.
Amps are a whole other world,but you may get away with going direct into whatever system you use for recording,most have a range of effects,etc. If you have to have an amp,some of the Roland Cube series are good,reasonably priced and plentiful.
Sorry if I've repeated ground covered by Neil.