It seems like you are activating the autobrake on takeoff. Not something you want to do. Make sure you only activate it just before landing. With the vertical speed, I'm not sure I can help you. What aircraft are you flying and do you have the ALT hold set or the master AP set?

I'm practicing takeoff with autothrottle indeed, I've tried it with TO/GA, but that doesnt do anything and when I tried it with speed hold, it seems to work fine, as long as the auto brakes are in the OFF position.
I've got A/T armed and I rev up the engines to about 60% N1, as my checklist tells me to, then release the brakes and activate speed hold, to have A/T perform the rest of the acceleration to the programmed speed: V2+15kias

Both checklists from FSX and the extended one I downloaded, tell me to turn autobrake to RTO, so that's what I'm doing...

Another thing, I want to start with the engines turned off, the checklist tells me that I need to turn the master starter switch to OFF, for chutdown procedure, but I cant find anything called Master Starter Switch and no matter what I turn off, the engines keep running.
Can anyone tell me where those are located? For now on the 737-800, but also in general, been trying to find them on other models too, but I can turn off everything, except for the engines...

I used to get this autobrake problem.  If you have a joystick with throttle or a throttle quadrant, and you are using the autothrottle, try to press your throttles forward or move them all the way up as the engines are automatically advanced to take-off power.  If your controls are down too far, the sim might register that as you pulling your levers back and the brakes will apply.