I dont mind paying the highest fees, what I care about is not to get stuck
It's more a question of selecting the optimum fee at any moment in time as it changes and there is no point spending more than you need to. Sometimes 10 sats/byte will get confirmed almost immediatly but yesterday 1000 sat/byte would have been needed.
Ill check my wallet and select highest possible fees, if there are recommended fees, what should I put there?
This site has a good estimate of what is needed at any time.
bitcoinfees.21.co
Edit: They seem to have messed the formatting up, scroll down to "Which fee should I use?"
What about Jaxx (iOS) and coinomi on android?
I'm not familiar with either of these wallets. I use Electrum and I prefer to use the advanced option to manually select fees. If that is available on either of these wallets then use that.