Pentax vs Sigma lens question

I have a Pentax K200D camera with the kit lens and I plan on buying another lens for action shots such as animals, birds and kids and have 2 lens in mind. I do most of my shooting in auto and jpegs. Still learning. Cannot spend more than $900 tops.
The Sigma 50-150mm f/2.8 EX DC HSM or
the Pentax SMCP-DA 50-135mm f/2.8 ED [IF] SDM

I think both are pretty good lens for what I want it for. Long zooms, fast speed for action and distance. Only 2 oz. in difference. About $75 difference.

The 50-200mm lens are twice the weight of the above lens and I've held one connected to a camera for a few days and it was too heavy for me. I want to be able to leave my new lens on most of the time.

Which of the 2 lens do you think would suit me better and why? Is there another lens I should consider within the same price range {$750 to $825 B&H}? Should I consider a faster lens? I've never had an f/1.4 etc. Should the 20mm difference be a factor in my decision?

This will be the only lens I buy for the next year or so as I only do this as a hobby and am an amateur. Thanks for any advice you can give me!