You have a very good question.
I use coinbase.com  . They are one of the largest and longest running exchanges at this time.
About as safe as they come.
It will hold bitcoin. etherium, and litcoin. They will be bringing on bicoin cash on October 1st of 2018.
Be very careful with your Key when you get it and print,copy.file.....in a safe place. One will be a group of random words in case your computer goes down and your random characters, ( that will be a key also) the you will have an address with random characters too. I will state " Address" so you will know the difference from your key and address.

I have been doing this for about 9 months. What an education!
You may want to look into a trazer wallet too. I just bought one. Don't get it from Ebay. not a good idea. It is like a flash drive on steroids. very secure.
Nuff info for now?

The guy who just answered your questions previously is very good too. I am going to be looking into some of the things he mentioned.  Wish you luck..Oh Yes, also triple check your address when you send coin. You will want to check to make sure it is the right one to the right person. You can lose coin very fast being in a hurry.