ok here goes may be wrong but you never know.
make sure both the FD and the auto pilot are on first of all.
as for the engines spooling down a little, remember it needs alot less power once in the air than to get it off the ground, if you watch the speed closely you'll see it shoot up to 250 in a matter of seconds, the nose dropping could be a cause of many a thing, forgeting to turn on the AP aswell as FD switch,
and also remember the higher the engine output the lower the angle of attack to climb
correct me if i am wrong and please reply if this of no help

I think your problem is you are setting autopilot too soon & in the wrong way.

Set AP in stages.

Don't engage AP until you are well established into your climb & more or less on your desired heading. 6-8000 would not be too far wrong as an altitude to think about AP.

Then set AP with an Alt of - say 10,000ft & an Airspeed of say - 100 kts above your current airspeed. & increase accordingly until you achieve your desires Alt, Heading & Airspeed.

Have you read the Tute I did ?
http://www.simviation.com/fstutorial_nav1.htm

Yes Pete!!  thats  it!   Thanks a lot!  the problem WAS i was engaging the autopilot too soon!

Bret! i turn on the F/D, but like you i find very little use for it!  except for the take off  where i follow only the horizontal wich gives me i good idea of the degrees to pull the nose up

F/D also turns confusing when landing! when i follow the vertical needle. better use the VOR ofcourse

But thanks a lot for your Data guys

Appreciate it 8)

I dont know why you think your stuck with the 2500 fpm after you set it, you can change your vertical velocity at any time.
one of the other problems you may encounter with the autopilot is being in an out of trim condition when you engage it.  If your aircraft isnt trimmed correctly when you engage autopilot it will start to adjust the trim. the problem here is it trims rather slowly and if you are still malking a control input (ie pulling back on the stick) you are actually fighting with it, and this makes things worse.
Now for the cheat, you can, in some aircraft use the autopilot to take off, this works in some aircraft and not in others.
set it for say 3000 ft with a 1000-1800 ft rate of climb.
start your takeoff roll, when you pass through 100 kts engage altitude hold and autopilot, once the aircraft has enough speed it will rotate  take off and climb to your set altitude. once she is stable in the climb you can change your desired altitude or rate of climb. also depending on the aircraft I would suggest a bit more flap about 20 this gives you a lot more lift.
As for the autothrottle backing off, if you r at 250 kts or even close it will back down, there may be fluctuations depending on what you are doing with pitch, but it should be Ok. I admit I havent flown the 737 much but these tips should work.
Juan, this is my job. I have been a USAF avionics tech for 25 years now (enlisted and civilian) and when I started out my specialty was autopilot. there is a lot of misinformation out there, not bad, but a lot of it is hit or miss results of people playing with it without really understanding it.
I have been tempted to open a School but just dont have the time. I have spent countless hours teaching people how to fly and navigate and using the autopilot I can make a new guy look like a pro in pretty short order I run with the VUSAFs (www.vusafs.com)
as Reach 10.  this org is dedicated to multiplayer flight.
recently we had a few guys having trouble getting their carrier qualifications and I put a carrier landing 101 post on our message board.  my instruction was based on using the A-6 but I have since found that I can trap with ANY aircraft that has a decent autopilot.  (ever see a 747 land on a carrier?)   Autopilot can be used for formation flying, air refueling and a lot of other stuff that people find difficult to do manually. recently we have played with a "Brigade Air Drop using 3 or more C-5's in close formation. we are able to change speed, configuration ( flaps) and altitude while maintaining the formation including through turns. some of us through practice can do this manually but it's easily done with the autopilot.

I apreciate you reply, and I like to help, just havent really been on the public boards much. finding more time for it lately.
as for links to aircraft, the VUSAFs hangar is locked due to the fact that the unit had a reputation for ringing out all the possible downloads and using the one with the most bang for the buck. that along with the server that we pay for allows for a fairly high-speed download.
all this combined to the point that there were a lot of non-members downloading form us. ( at one point we had only 40 members but were getting close to using up all of our monthly bandwith due to files being downloaded. and were looking at an additional monthly charge. This VA is kept alive by it's memebers and a very few of us actually throw our own money at it ( I myself paid for the hosting for the first year, I dont know what the current commander is doing for finance)
in any case Fate01 put a password on our hangar so we wouldnt incurr the additional charges. It's a shme we had to do so, but the only alternative is bite the bullet and pay for it, or possibly look for advertising (both unaceptable solutions)
In any case all of the aricraft are available either on simV or the other sites (yeah Pete this is your board so I wont say it ) I thought there was a list of the files on the site so non-members or recruits could search fro and download. I'll take a look and if it isnt there bang on a few doors to see if we can get it put up.  I'd give you a ilst but I'm not in a place where I can do that right now.