I moved about a year ago, because my girlfriend and I wished to get a place together.
So first I think as far as the, "Is a girl going to be weirded out?" question, I agree with what a few of the other posters have said. Assuming you're hoping for something long term, then obviously she's going to have to become aware of your interest in Transformers eventually. So get it out in the open as soon as you can, I say. Be proud! Have your Transformers on display!
The girl I am with now, I first met her online... So before we had even met in person, I said to her, "Yeah, I'm in my early 30's, I'm into sci-fi and anime, and I have huge collections of DVDs and Transformers." She didn't run screaming, and three years we are still together.
If I had tried to hide such things, perhaps I would have ended up trying to connect with someone who would be less tolerant of such hobbies, leading to trouble when they eventually came out. I'll admit, it may make your dating pool a bit smaller... but you'll have a better chance of ending up with someone who will make for a good long term prospect.
As for how to arrange them... In my case, it is true that the Transformers are a little bit all over the place... Just because there are so many of them! But even within those confines, they are arranged in what is hopefully a pleasing manor, rather then just being a big mess of robots.
What the heck, here's some photos. These are a bit old, as they are from shortly after the move. but things aren't too different these days.
First, a couple of panoramic shots just to give you an idea of what sort of layout I had to work with. (These are from early on in the moving in process, as evidenced by the fact that there are still boxes everywhere.)


Next is the entertainment center, with many Transformers on the right. (And a few Macross Valkyries on the left.) There is a shelf seen here with Optimus Primes on it. Those have since been moved, and that shelf now has Maketoys Green Giant and a Fansproject-augmented Bruticus on it. (With room for Fansproject's upcoming Menasor, as well.)

This nice big metal rack is a rescue from when I used to work for KB Toys. At the time of this photo, it had two shelves of Optimus Primes on it. For some time, it had three (after I moved the Primes mentioned above.) But it is currently back down to two and I made a decision to pack away the Bay-verse Optimus Primes. I know it won't be until towards the end of the year before it comes out, but I suppose I wanted to start planning on making room for the new Metroplex.

I've got some displayed in the bedroom, as well.

And we have one other room, which is for us kind of a combo office / spare bedroom. Of course, there has to be a few in there, as well.

There is one room that has no Transformers... I suppose in your new place I might suggest it isn't necessary to have any in the bathroom!
Finally, it should be fairly obvious, but here's my unsolicited recommendations on the actual moving process. Assuming your Transformers are out of their packages, I'd recommend getting plenty of big boxes and plenty of newspaper. Transform your guys into whatever seems their most compact and durable mode (usually vehicle mode), wrap em' up good, and pack them semi-tightly into the boxes. I had everything come through my move unscathed, and hopefully you will have the same.
Good luck in your new place!