Hi nitram, welcome aboard.
I'm actually logging in after quite a long absence from the forum, having built my machine some years ago and now just get on with using it.
What you want can easily be done by the kind of 3-axis CNC gantry router that is by far the most common type of machine you will see.

Do you want to buy a machine or build one?

As well as the machine itself you will need to choose a software package in which to do your drawing and that will then create the instructions (G-Code) that the machine will follow. There are several choices here depending on your budget, how much time you want to spend learning to drive it and the complexity of the projects you want to make. I'm sure others will add to the list below but these are the 3 packages I have some experience with:

Fusion 360: This is a very powerful, professional standard tool which is free for hobby users. It will do everything you want but is probably way more complex that you need and will require a lot of time to learn. I haven't mastered it and have never actually managed to complete a project using it.

Vectric Vcarve: A favourite with many people, but somewhat expensive. You can buy the Pro version or the Desktop version which is half the price but restricted to 24 inch square projects. I have the desktop version. Vcarve (and especially it's much more expensive cousin Aspire) is good for the decorative, bass-relief type projects.

CamBam: Inexpensive, quite easy to learn and very capable, especially for "engineering" type projects using 2D shapes cut out of flat material. This has been my go-to software for many years for designing things like clocks. It has a very good support forum and loads of free plugins which greatly enhance it's capabilities.

All these programs have free trial peroids so you can try them for yourself.

Kit