What would be a good exchange mobile app to use for trading coins?
Coinbase, coinbase pro
Or blockchain, blockchain exchange
Coinbase, Coinbase pro are strictly follow law regulations in the US. It is bad for now and future if you care about your privacy.
Blockchain has limited coins in the blockchain wallet and pair for your trades. You use their service but you almost won't get support to retrieve your accounts if you lose your wallet seed. Brute force to recover wallet is not for everyone.
Or would you recommend something else?
Binance. @mk4 suggested it for you.
It is a centralized exchange but have very good support process and you are allowed to withdraw 2 BTC every day without KYC. Many trading pairs on Binance, with Spot, Leverage, Future tradings. About 1100 trading pairs are available on Binance (click on Load more from the coinmarketcap link)
https://www.binance.com/en/support/articles/115003670492-How-to-Withdraw-from-Binancehttps://coinmarketcap.com/exchanges/binance/