Yes you are correct Google are not supporting Picasa going forward. That doesn't mean it will not continue to work it just will not have any new features added, so you don't have to panic about moving to a new software. Google do offer to transfer files to their Google Photo app so that is an option but i suggest you research other products as well. Adobe Photoshop is accepted as being the best but is of course not free, but definitely worth considering as a long term option.
The two free options i would suggest you look at are Gimp and Paint.net, with the latter possibly being a little more user friendly.
We in the meantime will consider all options available and make our recommendations once we have tried and tested them.
I hope this helps, but take your time before committing to a new vendor.