Most coins have their own wallets which you can download from the website of each coin.
Otherwise you can use an online wallet on an exchange but unless you're actively trading them I wouldn't leave them online.
All my crypto is offline on a hard drive. (It's all just Dash... Look into Dash if you haven't already.)
I found coinspot to be a reliable and safe place to buy cryptos. 6 months in and no problems.
If you use coinspot and are worried about polipayments.... Just know it's owned by Australia Post.
