Nervous guy--congrats on your new tractor and implements.
With 35 hp and 36 acres I probably would have selected a 60" rotary cutter.
Some people consider the 3pt hitch-mounted auger (aka post hole digger, PHD) to be one of the most dangerous tractor implements. Be careful. And be sure you have your BF pipe wrench and a long cheater pipe to extract an auger that's jammed in a hole.
I was going to suggest going with a 6 ft mower myself. I think he has plenty enough tractor for it anyway, unless he got the 4ft on purpose. Like if wanted to get it in somewhat narrow spots, then I would have probably suggested the 5ft like you mentioned.
As for the auger, you will need to come up with a good way to park it when not using it. THat is the most unwieldy and aggravating implement you could ever buy to use on a three pt hitch. You might want to consider either suspending it from a handy treelimb, or put a couple of 4x4x10's in the ground and add a cross bar over the top to suspend the PHD from.
Like already mentioned, the PHD is one of the most dangerous implements. When using it, make sure no one is anywhere near it except to position it, then have them step back several yards before engaging it.
Since this is your first tractor, take it slow and easy at first and become very familiar with how EVERYTHING and EVERY PART of it works. Give yourself time to learn how it reacts to the different commands you give it. Become familiar with the turning radius with implements attached, note how far out they extend from the tractor front and back.
Wear safety glasses, good leather gloves, and ear plugs when needed. If you're cutting some real tall grassy/brushy areas for the first time, walk over them best you can before starting mowing to spot stumps, logs, stumpholes, scrap metal, or any IMMOVABLE objects!!! Nothing worse than one front tire slamming into a hidden stump and then having both front wheels make a hard turn at speed!
Always wear a cap or hat too. Helps some when/if you mow right on top of a hornet or yellow jacket nest!! You can at least use it to swat the buggers away from you some! LOL.
Keep your cell phone with you in your pocket in case something bad should happen. At least that might give you a fighting chance should the unthinkable happen.
Oh yeah, keep reading tractorbynet!!! There is a veritable wealth of wisdom and knowledge here!! And the pictures are pretty interesting too if you love tractors! Good luck and be safe with it.