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 (even tough 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,...). And even then, it's a bad idea to hold a reasonable amount of funds on a desktop wallet anyways.

Since bitcoin is about personal responsibility and choice: I have heared reasonably good things about mycelium, but you should do your own research before using them. Personally, i would never use them for anything more than pocket change, but it's up to you to make up your mind.

If you want more security (and this should be your goal), you could look into hardware wallets like ledger... They have at least one model that can be used from your phone (and, eventough not everybody likes ledger, i think it's safe to assume they're a hell of a lot safer than any "real" smartphone wallet). They support a cured selection of altoins aswell.

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 idea, 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).