I’m not keen on the all-in-on devices. I like to have a bit of flexibility to swap and change components around, which the all-in-ones don’t give you. It’s a bit like buying a TV with a built-in VCR or DVD player - they never really appealed to me. I certainly wouldn't go for something like the HP Slate 21. It’s the worst of both worlds.
I think that if I wanted something smaller than a regular tower, I’d go for a decent laptop and use an external mouse and keyboard (and maybe an external monitor as well). You get portability if and when you want it and if you do as Bee says and go for an i5 plus 8gb of RAM you’ll have a nice fast machine. I’d also go for an SSD rather than a regular hard drive as it improves startup times enormously.
Don’t forget a removeable hard drive or two to do backups of important data/photos and keep one of the external hard drives disconnected when you’re not doing a backup to it, so that it can’t be infected by viruses or ransomeware.