If the remote desktop option doesn't sound right for you, about all you can use the laptop for is a remote display. To do that, you'd need a video capture card/software that can take the video output from the desktop, convert it into something like a USB signal to connect to the laptop, then the software on the laptop would then convert it back to video. Most likely as a window on the laptop's display at that and actual video quality may suffer unless you are willing to pay for something that will produce good quality video and may also have to play with the resolution settings on the desktop to get it to send something that looks good on the laptop since LCD screens don't typically produce well outside of their native resolutions. I'm not aware of a way to control the mouse and keyboard via the laptop other than the remote desktop option. Otherwise a wired or wireless keyboard and mouse would be the only option I can think of. Considering that, plus the prices on new monitors nowadays, you may be better off just getting another small LCD screen to use your desktop with and have it on the table. If you don't have plans to use the laptop for anything else, you may be able to sell it to recoup some of your costs (depending on specs and condition, as computer tech gets old quick in terms of resale).
Keyboards are all pretty much the same in terms of space, but I'm going to guess you like the idea of the track pad on your laptop for the mouse because it doesn't use much space. If that's a big concern, then you may be interested in a mouse like
THIS that lets you control the pointer with your thumb on a track ball, or
THIS. The latter is the same principle, just different ergonomics and I've known a few people that used it and loved it better than a regular mouse for regular use. Not sure how it'd work for gaming and such, and wireless versions will cost more too.
Good luck and hope you find a solution that works for you.