how easy it is to use Copay as a wallet that we can both share,
Copay is a true bitcoin wallet, not an account service. Secure your personal funds with multiple signatures, or just one
See also Multi Sig Use Cases
Multi-Sig Use Cases
m = signatures required to spend, n = signatures possible
m=1 and n>1
Could be used for small group funds that do not require much security. Least secure multi-sig option because it is not multi-factor. Any compromised individual would compromise the entire group. Group funds for a weekend or evening event might be a good use case. A shared wallet might also be fun for some kind of games too. Besides being convenient to spend from the only benefit of this setup is that all but one of the backup/password pairs could be lost and all of the funds would be recoverable.
Scary because no keys can be lost. As the number of signatures required increases the risk also increases. Could be thought of as hard multi-factor authentication.
Note that terms like "partner wallet" or "buddy wallet" are not generally used and understood. People are more likely to call this something like a "2 of 2 multisignature wallet" or a "1 of 2 multisignature wallet" respectively. Though the above terms are more general and usefully apply to many other values of m & n.
There have been desperate questions here from people who set up a 2-of-2 multisignature wallet and found their friend lost their wallet-password without making any backups. This meant all their Bitcoin became lost forever. So I'd suggest
Go for a 2-of-3 arrangement with a passive partner (someone you both trust not to use their signature except in pre-agreed emergency
circumstances. e.g. create a third key with your friend, and lodge the key, written on paper in a sealed envelope, with a lawyer)
If you must go for 2-of-2, walk through the backup and recovery process with your friend and make sure both of you are aware of the risks of not making a backup, or of not having tested recovery. You could easily lose all your money through a bit of carelessness on your friend's part.
I can't really answer "how easy" since I don't use it and that is rather subjective anyway.
Copay appears to be a popular wallet. It ought to be well-tested by it's users. It's probably worth trying out. If you find it doesn't meet your ease-of-use needs, you can always move your funds to a different wallet or import the private keys into a different wallet (saving tx fees).