Always have 2FA activated when you can. If someone gets your password, they will not get into your account without your phone.

Poloniex is safe to use, but you will need to do some math to get the orders right, you need to calculate them yourself. Don't be stupid and type buy 0.0001 BTC for 2 ethereum.

Also don't screw up the address, make sure it is the right address you are sending your coins too, you do not get a second chance when you send BTC if it is the wrong address. Check and make sure the first and last 5 characters you copy pasted in match the address you are sending to. Also send a small amount of coin first so you know you are sending it to a good address and it has processed successfully (eg. you buy $100 BTC, send $2 BTC to that address to make sure it is safe).

There are two types of storage, hot and cold. Hot storage is where you leave your coins on the exchange. Cold storage is where you keep them somewhere offline like myetherwallet or exodus.

When you can, transfer your coins from hot storage to cold. If exchanges go down, they may misplace or loose your money. That will be on you.

Also if you have any problems with exchanges, be nice to the exchanges. We are currently in an age similar to 1980s for the share market or 2000s for youtube, a wild west. Expect anything, and never invest money you cannot afford to loose.