Nice pics and even nicer looking machine!
Glad to hear the hydr fluid was clean.
A couple of thoughts come to mind...
You might want to run it for awhile once you're satisfied all is ok, then change the oil again.
If you want to be fussy and you've room to remove the oil pan, you can manually clean out the stuff that never comes out!
Remember to use antifreeze made for tractors when you get to that point.
Hoses should be checked and replaced and all the wiring inspected for damage from critters.
There are threads on here about products to repel critters too.
Get a nice grease gun. I have the Ryobi electric, but I like to use a handgun first to "feel" the zerk fittings and ensure they are taking grease.
I also favor plastic zerk caps for added protection. Zerks are easy to replace if you find a clogged one.
If you find pins that won't take grease, that's another discussion. Best to find that out before you go into service with the machine. Also look for worn and loose pins/bushings in the bucket, hoe and such.
Lubricate all the mechanical joints you can find as well with oil/grease. I find that it helped me get very familiar with the machine digging around it with lubricants.
You might consider Fluidfilm or other to help stave off rust and corrosion. Others will likely offer their experiences and products.
Get a battery maintainer too. Millions out there to choose from. I have used the Battery Tender with good results. I also use the Harborfreight version with my motorcycles.
Check the front axle for oil. It will use regular 80-90 weight oil. You may want to drain it and refill just to be sure it is filled properly. If there's lots of wear, the old oil will look like there's glitter in it! Once you refill, you may find that seals leak and that again is another story.
This forum also recently had some discussion on diesel additives you might find interesting. Winter is coming and diesel can gel and it can also get bacteria in it.
Air filter should be checked for cleanliness and for any critters' nest residuals.
'hope this helps...