Well... That's quite a hard one... I have no experience with holding loads of altcoins on a phone. Generally speaking, i'd say it's a bad idea... I personally don't believe those wallets are as thoroughly vetted as open source desktop wallets (eventough that's just a gut feeling), combined with the extra attack vectors (easy theft, a lot of times just a 4 digit pincode as protection,...).

But i have heared reasonably good things about mycelium, but you should do your own research before using them.

If you want more security (and this should be your goal), you could look into hardware wallets like ledger... They have a couple that can be used from your phone.

Personally, if i were you, i'd probably use a wallet like mycelium (or even an exchange wallet) to receive coins, swap them for BTC the very same moment i receive them, and then keep them on a properly generated paper wallet or a hardware wallet. Bitcoin is money, keep it safe. Don't cheap out on $100 for a decent hardware wallet when you're storing a couple thousand dollars worth of crypto... It's just not a good idear, and you'll end up losing funds sooner or later (and at this point you'll wish you had spend $100 on a hardware wallet, or a couple of hours learning how to properly generate and secure a paper wallet).