First of all, take that bike out & give it a whirl on a non-commute day. Just see how it feels & maybe something specific will come up; if it does, then ask here.
Also, take it one step at a time. There's a lot of info here, take your time to read & decide what to tackle first & get that under your belt before moving on. As you ride more, I think it will become apparent to you what you want to focus on next.
I learn best from books, so I'm going to recommend Zinn & the Art of Road Bike Maintenance, by Lennard Zinn. It covers probably way more than you want to know, but it's also broken down into micro-sections. I read the whole thing like a novel when I got it, but I'm weird like that. It's really a reference manual.
For example, this weekend I looked up the How to Clean the Bike section, so I would know where all the holes in the frame & critical grease points were. It was under a page long. Also, the illustrations are fantastic!
You have a lot of advice from everyone on the maintenance part. Here's some other stuff that might be helpful:
You are lucky that you can ride on that trail. That takes a lot of the stress out of riding. My biggest issue is with traffic. It's scary! In my state (CA), bikes are required to ride on the right side of the road, in the street, and obey all traffic laws. Those over 16 are not required to wear a helmet, although it is a good idea & most do wear them. You may want to check out the cycling laws in your area.
Let's see...gear. For a 9 mile ride, you may want to carry water with you. Probably you have a mount or two for a water bottle cage, if you don't already have the cages installed. They just screw on, so you can do that yourself. Or carry it in a backpack or strap it to a rack.
Shorts with padding are probably advisable. I only go <3 miles at a time, so just wear street clothes. Other than the shorts, you can get away with street clothes for the rest. Unless you have fancy pedals & want to clip in; then you need fancy shoes. Not required, but nice if you want to a smidge go faster.
Most other gear is optional; it just makes your ride a little nicer, more efficient or just plain fancier. For example, you can get away with a regular windbreaker, but the bicycle-specific ones have a longer back to cover the gap above your waistband, where a normal shirt ends when you are leaning over the handlebars. Depending on what you already have, you may not need (want) that.
I am finding that I get real sweaty on my back when wearing a backpack; this is only going to get worse as the summer wears on. So am now looking into racks/baskets/panniers. Sounds like this may not be an issue for you if you are changing when you get to work, but thought I'd mention it.
Later on you might need to look into lights/reflectors, but with the daylight lasting so long, this may not be an issue for you. The other thing you might need later on is rain gear.
Spare tube, patch kit, tire levers & pump are required. There are some other basic tools (allen wrenches etc.) that are good to carry, but if you don't know what to do with them, they're not going to help you. So get the tools as you learn what they are for. They sell little under-seat bags that can hold these items, but they could also go in a backpack or wherever.
There's a lot of stuff you can get for your bike...I think you already have the very most essential gear & pointers for the most essential maintenance. Enjoy the journey!