My first shuttle launch watched live was this past one which took place at night. I live about 20 minutes from the Kennedy Space Center. I'm new to Central Florida and live in Brevard County.
Your ticket gets you entrance to the facility for tours/attractions, and a launch viewing from the main complex if there is a launch that day.
There is a special ticket you can buy which entitles you to transportation to a part of the complex that is only 3 miles from the launch pad, rather than the 7-mile distance between the pad and the visitor complex. (They pin a special tag to your shirt, sort of like a VIP thing.) If you purchase this ticket and the launch is scrubbed, there is no refund as it provides only transportation to the closer viewing site.
If you buy just a regular admission ticket and the launch is scrubbed, as it was with the last shuttle launch, you still have the value of the ticket to go towards all attractions at the KSC. The KSC has so much to see that I recommend making a 2-day visit to the complex.
There are various places near KSC but outside of the complex where you can park your car and watch the shuttle go up. However, the KSC complex is your best bet.
I would also like to recommend KSC's various gift shops; there are 3 along the tour but the one at the main complex is the largest--save your souvenir buying for the end of the tour since that is where you'll have the best selection anyway. Their prices are absolutely fantastic--I was quite shocked to see how inexpensive their souvenirs are. I took some relatives who "cleaned house" basically, especially seeing how much more souvenirs cost at WDW. KSC has beautiful color posters for something like $2.95 each, which could easily be framed and offered as a gift or to put in your child's room. (Posters are easy to transport back in your suitcase, too.) Most everthing else was also similarly reasonably priced--shirts, hats, toys, books, videos, key chains, "astronaut food," ornaments--you name it.
When I went for the evening launch it was cold. It should be relatively cold in March at that early hour, and you may be sitting on a cold metal bench, though many people brought their own lawn/lounge chairs, etc. (for the main complex viewing, not the closer launch pad viewing). Dress warmly and bring a blanket or two if you can. The suggestion by another poster about staying at a local hotel was a good idea considering the launch is so early in the morning. You don't want to be driving that early from Orlando.
Speaking of driving--it is definitely NOT 45 minutes to KSC from Orlando. I'd say at least an hour, and probably longer considering morning traffic on a weekday. The main road from LBV or Orlando is the Beeline Expressway (now called the Beachline) and is also a toll road but more towards Orlando. The tollbooths can get backed up for days during commuting times.
Finally, I asked a family member from out of state what he thought was more spectactular--Illuminations at Epcot or the night shuttle launch. "The shuttle launch for sure," he replied, with a big smile on his face.

To see that ball of fire trailing behind the shuttle as it went towards space, its accompanying sonic boom shockwave, and the cheers of onlookers, well, to me that trumped anything Disney could produce. In fact, the KSC is coming out with a launch-type attraction in the near future that will trump Disney's Mission Space.
Hope this information helps.