I have a imac 27" macos 12.7.6 Can I upgrade without getting a whole new system?

What model year is this 27" iMac? Check Apple Menu ➜ About This Mac.

Depending on that, will be whether you can upgrade to a newer macOS version or not.

No, you don't need a Mac mini, unless you want an entirely new computer. A Mac mini is not an upgrade for an existing computer. It's a whole computer in and of itself. It's like saying do I need to buy a new iMac to fix my old iMac.

You can buy any new keyboard and mouse if you want and use them with your existing computer.

As to the slowness, please post an etrecheck report of your current iMac and someone may be able to help you fix or at least reduce the slowness.

click here ➜ Using EtreCheck - Apple Community

Servant of Cats wrote:

Note that many of the current Apple keyboards and mice require Sequoia (!!!), so if you need a new keyboard or mouse, you might be forced to buy a third-party one.

This is indeed true.

But any third party wired or wireless keyboards should work fine.

Though most will have Windows specific keys (Win, alt, menu) instead of option and command. If you need one with Mac keys specifically choices might be a bit more limited. Both types will work fine, and you can use the windows key as command and the alt key as option though.

The 2015 iMac cannot update pasa macOS 12.7.6 Monterey. It’s at the end of the Operating System update path.

Please post an Etrecheck report, and we may be able to address the slowness issue.

click here ➜ Using EtreCheck - Apple Community

Note that many of the current Apple keyboards and mice require Sequoia (!!!), so if you need a new keyboard or mouse, you might be forced to buy a third-party one.