I wonder if anyone could give me advice on which drum computer to buy to accompany my guitar playing (mostly at home). I need it for practice/ songwriting when I'm on my own.

Just something simple I can plug in a amp and works

Preferably I want to be able to program a complete song beforehand (with a different patttern for the chorus, bridge etc. and where you can just press play and play along... If this exists?

I'm not familiar to the drum computer market so I hope you guys can help me out

What you need is a VST drum sequencer for the DAW you will be using to record. These are popular:

Superior Drummer
Addictive Drums

I haven't tried Superior Drummer or BFD. EZD is ok but i find Addictive to be much more versatile. You can check out the link in my sig. Drums in both of those recordings are done with EZDrummer in Cubase 5.

I'll look into that software. But I actually meant hardware, something in a box. Although i'm gonna use it mostly at home I want it to be mobile and useable without computer.