Dead phone

Sigh, my phone seems to have worn out. I thought this one had been treated fairly well, with a case, and not suffering any disastrous drops. But now when I turn it on, it reboots again either immediately before finishing the boot sequence or as soon as I open an app.

I tried removing the case and waggling the buttons, and doing a factory reset and that didn't make a difference. Is there anything else I should try?

Assuming I need a replacement, what should I get? Probably a recent android phone. I used to always get nexus but pixel seem to have got expensive.