Traditional compact cameras are a bit of a dying breed thanks to the use of phones.
Avoid the very cheap ones sold on Amazon, even if you recognize the brand - “Polaroid” or “Kodak” for example are camera brands that have been sold on to the Chinese and now appear on cheap tat.
I would suggest you have a look on MPB for something second-hand - no point in paying full retail any more. I buy professional cameras and lenses from them, or as “refurbished” from Fuji UK.
https://www.mpb.com/en-uk
Fujifilm compact cameras like the X100 series are really nice, but they command a premium since they have been taken up by the hipster crowd. 
It depends on your budget as well. A Canon Powershot compact with a zoom would be a good carry-around camera. Bear in mind that older (and cheaper) ones will have slower autofocus and poorer low light performance.
Panasonic (Lumix) or Sony would also be viable options.
If I was buying a “one size fits all” camera I would be looking at an interchangeable lens mirrorless camera.
Fujifilm are my personal preference, as I think their colours are really good (especially skintones) and they are nice to use. Something like a Fuji X-E2 or X-E3, or if you don’t mind a bigger form factor, an X-T1 or X-T2 perhaps. At one time I shot whole weddings with a pair of X-E2s so they are more than capable, if not super-speedy to focus in modern terms.
https://www.mpb.com/en-uk/category/used-cameras/mirrorless-cameras/fujifilm-mirrorless-cameras
Alternatively the Micro Four Thirds system is worth considering (Panasonic-Lumix, or Olympus).
The sensor in these is a bit smaller but they are nicely made and quite compact.
https://www.mpb.com/en-uk/category/used-cameras/mirrorless-cameras/panasonic-g-mirrorless-cameras
You will need to add a lens but that need not be too expensive - there are consumer-level “kit” lenses for both Fuji and MFT. In the MFT range you can mix and match e.g. an Olympus MFT lens will fit a Lumix body.
The advantage of an interchangeable lens system is that it gives you room to grow if the photography bug bites - you can add a longer zoom lens, or one of the nice compact prime lenses.
Ask if you have questions!