Welcome to TBN and the wonderful world of the Class III NH Boomer.:thumbsup: I think you will find the TC35D with 16LA loader to be a marvelous addition.
Lift the hood and look on the bottom for a decal with the maintenance intervals. At just over 600 hours, your hydraulic fluid should have been changed once and it is ready to be changed the second time. You'll need 7.5 gallons (not 10) to do this job, plus one hydraulic filter and one HST filter. NAPA and O'Reilly Auto carry filters. Wix makes filters that will save you a few dollars over NH filters, but I use NH filters on my tractor. You should also do a check of the fluid level in the front axle. The front axle and drop boxes should probably be drained and fresh fluid added. If the engine oil looks okay, you might wait on that change, but the safe way is to change the engine oil and filter.
Look on the tractor ID plate on the left side under the operator platform and get the Unit Number instead of the Serial Number. The Unit Number identifies when the tractor was built. With your serial number, I'd guess it's probably built in 2001 to 2003. The total hours is a whole lot more important number than when the tractor was built.
If you are getting oil on top of your front axle, it is probably coming from your HST cooler or the lines going to the cooler that sits right in front of your radiator. Some of this model tractor had horrible problems with battery acid damage to the radiator, HST cooler, or fluid lines. Some HST coolers were not built well and develop cracks around the hose connections on top. Investigate the cooler as your most likely source of leaking fluid.
A second place that can leak is the power steering hydraulic pump and lines over the front axle. Your reservoir is under the hood on the right side of the tractor and has a dipstick when you remove the lid. Inspect the reservoir area and hydraulic lines for leaks.
You can find manuals on eBay from time-to-time, but I think the Tractor Operator's Manual and the 16LA Loader Manual are each less than $40 when ordered from your NH dealer. The Repair Manuals will set you back over $300. There is a CD available with non-paper manuals for a significant savings over the paper manuals.
Hopefully some other Class III owners will post and give you their thoughts. I sometimes feel guilty for dominating Class III discussions, but I do it just because I love mine so much and want everyone else to have a similar good experience.
Here's a link to a thread describing the structure of the
Unit No.