I am looking for some reliable wallet service / application with multisig possibility.
You definitely shouldn't be looking for an online 'service'.
If you don't own the private keys, you don't own the bitcoins.
Me & my friend are about to start a small business
We want to create a secured wallet so that none of us independently can spend the money, ie to spend the money we have to put 2 signatures ( his & mine ).
Especially in this case.. you should DEFINITELY NOT use an online wallet.
Create a 2-of-2 or 2-of-3 multisig with a desktop client and keep the private keys secured offline.
I know that it's possible, but at the same time, I don't want to use things like Bitcoin Core.
So I am searching for more UX friendly alternatives and, of course, reliable ones.
Well.. you can either have the most UX friendliest which is probably an online wallet. But this WON'T be a secured one.
If you want to own your BTC yourself (not the website provider) and want to have them stored securely, set up a multisig using a desktop client.
You don't have to download the whole blockchain. You can use a lightweight client (e.g.
https://electrum.org/#home).
There a lot of tutorials available online how to properly create a multisig wallet. This does take 5 minutes of your time.
The reward for those 5 minutes is a secured storage solution instead of some 3rd party wallet service (which would be dumb when running a business).
If you technically don't understand anything at all, i doubt you will be successfully able to accept BTC payments or whatsoever.
In this case pay someone to show it you step-by-step..