I just bought a great "commuter" style puncture resistant 26" tire for my beater bike at Wal-Mart for $25 (it is a "slick"). That is half what you would pay in a bike shop. Your proposed bike is a great starter kit. Give it six months and when you find you are hooked, go visit a real bike shop and spend some real cash on a real bike. If you can afford to spend the cash, the upgrade will be stunning to you after riding for six months on your beginner bike (at least, that was my experience).
Fenders are a requirement as riding home in Florida in the Summer means riding home in the rain at least two or three times a week. Make sure your backpack is waterproof, or pack your gear in a "wet bag" before you put it in the backpack (this will also keep it dry from your back sweat).
I used to live on W Hillsborough (just West of the Veterans Expwy) and I work at the International Mall. Hillsborough Ave is a great road to ride on because it has a 4 foot wide shoulder so you can ride on it both ways. Going into work, go East on Hillsborough Ave all the way to Lois. Make a right on Lois and it ends at Hillsborough Community College (HCC). Instead of Lois you might consider Westshore on the East side of the airport - that road used to be unrideable do to extremely narrow pavement, potholes, steep drop offs on the shoulder, and bumper to bumper commuter cars rushing to get to work. But they repaved it after I moved away and it might be better now. Check it out by car and see if it is better now. Lois is a little better because it is slightly less traveled, has a lower speed limit and a couple of lights which slow down the traffic.
Either way you come out at HCC and there is a very wide sidewalk you can ride past HCC. The sidewalk disappears at the police station just a block short of Dale Mabry. Take to the road when it is clear. It is a short distance but it is full of cars rushing to get on Dale Mabry, so sometimes you have to stop and wait for the road to clear before you take the lane. There is a narrow but rarely used sidewalk along Dale Mabry until you reach Boy Scout. Normally I would say never use a sidewalk but this one has no cross streets or entrances and is rarely occupied, so it is safe to bike and and you can go as fast as you want.
Make a right on Boy Scout and use the road for the half a mile to the first traffic light at the Corporate Centers, where you can make a right and ride through and the International Mall on a 25 mile speed limit road with four lanes.
When coming back the other way for that half mile section of Boy Scout, I would go off road and ride in the grass on the left but watch for potholes - a couple of years ago they dug holes along the road to bury cable and a year later the holes were still there, covered with grass. Nice little hazards.
During the Bucs football season they open up a parking lot with an entrance along this section of Boy Scout. When that is open you can take it as a shortcut - it goes from Boy Scout all the way to HCC so you can avoid Dale Mabry entirely. It cuts almost half of your offroad ride in the grass.
From the International Mall you can ride Westshore South. There is a sidewalk but I wouldn't recommend it because there are so many side entrances into business parking lots that in this case, the sidewalk would be more dangerous than the road, unless you ride it at walking speed - 5 MPH. My advice would be to ride in the road and claim the lane. That stretch of Westshore is nasty, but there isn't much better in the way of alternatives. I ride Lois South past Kennedy every day on my way down to Gandy Blvd to ride to St Pete. If you work on Cypress, you could ride Lois to Cypress and go right on Cypress, but Cypress is not much better than Westshore. I would try both routes and see which feels better.
Also, I would recommend you read this article:
http://www.floridabicycle.org/freedomfromfear.html