I have this old Tulip notebook with 40GB hdd and originally Windows 2kPro installed on it.
What Linux brand do I use here?
Linux Mint seems a bit to heavy.....

Linux:
Tiny Core Linux
Puppy Linux

Not Linux:
Kolibri OS

Slitaz, Antix maybe a few others would work OK on it. Might not be too fast. A swap file would sometimes help even on installers.

I think everyone here has their go to minimal distro. Each has good points and bad. Worth it to play with a few of them.

i'm sorry, but is this a real computer (laptop)?
or some sort of pre-tablet palm device?

does it have cd, usb? or how are you plannning to install?

antiX should be fine. I wouldn't go for SliTaz, Puppy or TinyCore, they load their filesystem into RAM and you don't have much of that already, so better stick to a "traditional" approach with having the filesystem on a disk.

Heres an artical that covers oldies -- and this artical is old too because it makes mention of CrunchBang, but it maybe worth a read as their are still Distos pertaining to your situation.

very important aspect!
i never thought of it.

The other side of the coin is that you speed up it a lot running from ram. Then swap file/partition would assist if you go out of that.

You won't speed it up in general. The only thing you actually can speed up when loading the filesystem into RAM is application load times. You won't speed up actual application execution and with wasting already constrained RAM by using it for the filesystem you may actually make the system much slower, just because the system may need to start swapping much earlier. And swapping is something you really want to avoid, since it usually, due to the slowness of mechanical storage especially on older systems, slows the system down to a point where it becomes virtually unusable.

A forum made just for you. That you should join.

http://linuxbbq.org/bbs/index.php

For those recommending AntiX. Our minimal specs have changed.

From http://antix.mepis.org/index.php?title=Main_Page