I have linked below a site where you can download the manual.

Since it's a Sear's product, you should be able to contact them for help getting parts. I Googled Craftsman YT3000 and found several hits. Once you get the manual, hopefully it will help with the parts you need.

Here is a link that might be useful: Craftsman Gas Powered Riding Lawn Tractor Operator's Manual for Craftsman YT 3000 Lawn Mower

The ONLY way to know exactly which Craftsman machine you are referencing is to post the technical model number found under the seat.
All those LT, YT, and GT prefix numbers are just marketing numbers and the same model designations are used over and over again from year to year (so long as that model enjoys good sales).
The technical model number removes any trace of doubt as to how your tractor is built.

Ditto what mownie says.
Number should be 917.xxxxxx.

Seat switch might possibly be able to be shimmed/adjusted to provide more positive plunger travel.
Steering tends to be pretty weak on these, with the various plastic bushings in the wheels and sloppy steering sector etc.
You pretty much have to look to isolate where the major looseness is. Are the wheels "sloppy" on the axle etc.

And, if this is a manual gear transmission, a lot of time issues of wanting to "jump out of gear on take off" are simply due to the transmission gear selected not actually being fully engaged. You may think it is engaged but the internal parts are only "sitting on the edge of engagement" and the parts get pushed back when you attempt to take off.
About all I can suggest along that line of thought is to try and keep a push on the shift lever toward the gear you want while you sort of jiggle the clutch pedal up slightly but push it back down. Sometimes that trick will entice the transmission to allow the gears to reach full mesh detent. Since you say it does not jump out once you successfully get going, I think you may not be getting it fully into gear sometimes.

Thank you all for your replies. I noticed that I accidentally typed 3000 instead of 2000. I now have the model number: 917.289101 and serial number: 050109Do12734.

I really appreciate the advice offered. we no longer have a sears in my town and the next closest is more than an hour away. I do not have a the ability to haul it anywhere. i am going to try to find a manual on this thing.

Re: The seat switch-
Make sure the connector is fully seated.
That's likley not the problem, but it's cost effective to check.

IF you didn't get an owners manual with it, you can at east get some "exploded views" at
searspartsdirect.com

The Sears website indicates that model 917.289101 has a hydrostatic transmission, so I'm not sure what you mean when you say it kicks out of gear on take off.