You do NOT need a $4000 trailer!
Re renting: Good in the short term but not smart over the long haul. You'll need the u-haul for 3 days minimum (for a single track day) since you need to be there at dawn and won't get home until that night. For a two-day event, you'll need the trailer for four days. So the cost is $45 - $60 per pop and it never ends.
Many, many people, myself included, use the folding Harbor Freight trailer. $300 all day long, plus the cost of a sheet of plywood, and it stores in the back of your garage. It's entirely acceptable for trailering one or two bikes. Remember, the bike, ramp, and whatever else you're likely to put on the trailer (EZ-up) total 450-500 lbs, tops. That's nothing.
And you don't need a big vehicle, again because you're not hauling much weight.
Here's my rig. It gets me there without any issues whatsoever, and gets 30+mpg while doing so. About the same cost as a single season's worth of trailer rentals, and less hassle.
If you have a pickup (I think you do, based on your post), then all you really need is a good ramp, the longer the better. I'm one of those pussies who thinks that most of what you see on the Interwebz about loading is insane... balancing a 400-lb bike over your head while you step up... screw that. I just put the bike in gear, stand beside it, feather the clutch and power-walk it up the ramp. Works fine on my trailer and would work just as well on a jacked-up 4x4 if the ramp were long enough.
Re insurance.... better triple-check. Highly unusual to have coverage for anything track-related. Just accept the risk.
Re suspension... sure, get a baseline setup. But the first day or three (or five) are NOT ABOUT THE BIKE. They're about you. I can't emphasize this enough.
Focus your attention and money where they're going to do the most good. That's on the rider and track time. If you have to choose between upgrading the bike and going to the track, GO TO THE TRACK. If you can afford instruction, GET IT. It's a much smarter way to spend your money at first.