First, congratulation on your purchase. If you are like me, then you will find many uses for the backhoe, at least for several months then it may slow down a bit. I have had mine for over 18 months and still find enough uses for it that I have yet to remove the backhoe from it, but I do have another tractor for 3 ph work when needed.
As with all tractors, the most important thing to do is after 10 hours, check all the bolts on rims and FEL/backhoe mounting brackets in particular. These all have a tendency to loosen up OR not be completely tighten by dealers. After doing that give all the other bolts on the tractor a test for tighteness. I may have the terms wrong but I had the final drive bolts on the front axles loosen off on one of my tractors. The are the bolts on the back side of the housing that holds the front axle. Failure to keep any of these bolts tight can cause some serious NON-WARRANTY covered damage to the tractor.
Grease ALL the grease points even though these should have been done at the dealer. The grease zerks on the FEL and backhoe must be greased every 10 hours (daily) of operation as a minimum to prevent pin wear. Failure to do so will leave you with a bunch of sloppy joints in the equipment in a very short period of time.
If you have an air compressor, I would suggest that you get a pneumatic powered grease gun as it is so much easier to hold the tip with one hand and just pull the trigger rather than trying to hold the tip on the zerk and pump at the same time. Many of the zerks will be located such that you will need to have a flexible hose on your grease gun which makes you need a partner to hold it while you pump. A pneumatic gun doesn't need two people to operate it. Some folks prefer to use the Lincoln battery powered guns, but at over $200 cost, I will stick with my $20 pneumatic one.