Headstock looks like an Edwards one – are they maybe the cheaper versions of them, rebranded?
At that price you can easily afford another £40 or so to get a full set up done by a local guitar tech. It may not need it though…
Things I’d look for are:
The strings buzzing when holding notes at different parts of the board, or the strings being too high off the fretboard.
The intonation – using a tuner ( you can get an app on your phone – BOSS one is good) – check that the note when the string is open is exactly the same as the one at the twelfth fret. You can watch some videos on youtube to see how to fix this if they’re off.
Run your hand down the side of the neck, if the ends of the frets are jaggy they might need filed. If you have blood on your palms after, they most definitely do.
Pull the strings up from the fretboard by quite a lot. You’ll not break them. Have a look and see if they feel loose in the nut (where they are held at the top of the neck). That might need fixing. This technique also stretches out the strings and stops them going out of tune (I do this after changing strings).
Do the tuning pegs turn OK? Are they notchy?
Look down the neck from the headstock end. Is it warped from side to side? (it should have a bit of a bow on along its length).
Plug it in and check all the switches and controls work OK and aren’t crackly. Does the guitar lead sit in its jack socket firmly?
Second last thing is to check the … oh damn, forgot the name… the bits the strap goes on. Are they loose? They might just need tightened up with a screwdriver.
Now crank the amp up as loud as you dare, and turn up the gain. Make sure you’ve not split the humbucker with the coil tap. Play a riff then mute the strings. Do you hear a high pitch squealing? (not rock n roll feedback stuff, more dog whistle)? That can indicate the pickups are microphonic. That’s quite possible with a guitar at that price.
It’s only important if you’re going to be gigging with it, or it it happens at the volumes you play it normally. The pickups can get wax-potted, or just replaced for better ones. I wouldn’t worry too much about this at first though – that’s more an issue for down the line.
That’s the basic checks for a cheaper guitar. Apologies if you know all that stuff – wasn’t sure of how much you know about guitars.