All I want to do is to be able to store most of the coins and tokens as in Binance,
You can use
Trustwallet or
Metamask if you really want to store most of the coins or tokens that can be traded in Binance. Typically, these wallet can store most of the tokens that are created under ETH network and can also be traded with some of the available
DEX's.
and to be able to trade smoothly with low transaction fees.
I don't think this is currently doable. Utilizing some of the top decentralized exchange such as Uniswap, Pancakeswap or 1inch will probably cost you more than the value of the tokens/coins you are exchanging. Currently, ETH network is congested so does the gas fee.
I do not want to use the standard centralized exchanges that everyone uses because I do not want to face situations where my assets are annoyingly frozen by others, nonsense documents are required, and especially when I have to verify the source of my assets.
Using Binance will only require you to submit KYC/AML verification if you exceed a daily withdrawal limit of at least 2 BTC or if you are going to use P2P Exchange. If you are trading below that amount of threshold, I think you will have no problem trading your assets. Also, being a Binance user myself, I still do not encounter such issues in terms of asset freezing, or maybe I am just lucky that I do not violate their terms of service until now.