Welcome to the sport!
I'm now about 4 years into car ownership and I've gone from initially borrowing an open trailer to purchasing a used steel open trailer to owning a gooseneck enclosed version and a larger tow vehicle. (Slippery slope... : )
Each stage and approach has its advantages in hindsight. With no trailer, I was obviously at the mercy of a generous friend but I didn't have to worry about storage.
The steel open tandem-axle trailer with a box and tire rack is great. It towed easily behind an older F250 and carried much of what I needed before I had many extra spares, wheels, tires, etc. I still have it and use it to transport the cars locally, if needed. It's small enough that I can store it inside the shop space I rent. It wasn't expensive, ~$1,100 and an afternoon of rewiring and paint. I know I could sell it if/when needed and get all of my money back.
On to the gooseneck enclosed. I bought a clean used one and I couldn't be happier with it. I've spent the last year tinkering and customizing it for our use. I upgraded to a RAM 3500 along the way. There are many more spares to carry now and much more packing required. It is, however, extremely convenient to drop everything off post-race and get back to it a few days later when I feel like unloading, instead of having to do it late night on a Sunday.
Know this, you'll likely grow into whatever platform you pick. I'm surprised at how crowded the doghouse was on this last SIC weekend...
Funny thing, as much as I like today's approach, I do sometimes miss how simple it all was initially. Here in the southeast, we're very fortunate to have great support at the track from teams like OPM Autosports, Panic Motorsports, BSI Racing, East Street, Trackside Tim, etc., so newbies like I was can go bug Tom and Steve for parts that I never imagined I'd need to bring... (Still do, BTW. Thanks, Tom, for that end link bushing my crew chief forgot to secure after the rain session...)
Make friends at the track and build a good support system from the onset. A twelve-pack of cold beer will go a long way in that effort... SM is great class that pulls together to help out and the friends you make would prefer to beat you on the racetrack instead of driving past you parked in the paddock.
Good luck and have fun!
-Kevin Bailey