For a basic transfer, it's probably best to use a gas tracker like:
https://etherscan.io/gastracker to check on costs. It's about $6-8 at the moment. The average tx cost is going skew much higher because of DeFi transactions. Uniswap V3 is scheduled to deploy on Optimism potentially in a few weeks which may help alleviate fee pressure (although as you can see from the linked gas tracker, Uniswap V2 is still consuming a large portion of txs). The bet is that a combination of L1 and L2 improvements will bring transaction fees back to reasonable levels in the next year or so. If it doesn't, there are a host of new competitors like Algorand or Solana that are looking to supplant Ethereum (and do currently provide much higher transaction throughput and lower costs).
In general, fees go up as the token price goes up since fees are usually charged as a function of transaction size or complexity, and also fees rise as a protocol hits its tx limits, but not always. Nano is an interesting cryptocurrency that is fee-less (although they just had to roll out an emergency update to improve spam resistance), so it's possible to design a fee-less system, but it's certainly even more experimental atm.
There are, however a number of cryptos that currently (and by intent) have <$0.01 (sometimes significantly less) fees. This includes (just going down by market cap): Ripple, Bitcoin Cash, Stellar, or Dash. For transactions, even though fees are a bit higher (about $0.06), I like Monero since it's one of the most private and widely used cryptocurrencies out there, and it's fees have actually significantly decreased due to technical improvements in transaction efficiency, dynamic blocksize, and an algorithm that can actually reduce fees as volume increases.