+1 for Johoe's site. It's the only site I use for deciding what fee I want to pay. There is a great guide on how to understand and interpret the graphs on 1miau's post here: https://bitcointalk.org/index.php?topic=5182906.0 (scroll down to item 5).

Every site which tells you a fee is using some sort of automatic algorithm. Sometimes they are quite accurate, other times they are not. Only you know how urgent or not your transaction is, and it's far easier to see if the mempool is filling up or emptying if you eyeball it yourself. If you really just want a site to tell you a fee to pay, then pick https://www.coinb.in/#fees.

The transaction will almost always confirm eventually, you might just be waiting a couple of days. In the event that the mempool becomes very full and your transaction has a very low fee, it will eventually be dropped from all nodes and you can simply try to spend the coins again. If you use a wallet like Electrum, you can enable a feature called RBF or Replace By Fee - with this enabled, if your transaction is taking too long to confirm, you can boost the fee to have it confirm faster.

This site is only useful if you look at the charts yourself. Their suggested fee at the bottom is usually way too much unless you absolutely need to get in to the next block. At the moment their suggest fee is 22 sats/byte, which would put you around 0.05 MB from the tip of the mempool.