I've noticed that most transsexual women admirers (and I use that term loosely) prefer per-operative transsexual women. Though you all do know that almost all per-operative trans women are planing on having SRS but are unable to do so for one reason or another. They never liked the fact that they have (as I've come to find out a lot of girls refer to their penis as this) a "tumor" between there legs where a slit belongs.
And from my experience of the course of my own transition, most of the transsexual women that I've encountered (be it through support groups, online chat, or other social situations) are pre or post-op.
And further more, don't want to use their penis at all. And just like a lot of cisgendered women, some pre and post-op girls are exit only in reference to the back door. My best friend is one of these pre-op trans girls. She will get her surgery when she can afford it, and her back door is off limits.

Non-op is probably more in tune to what most of you are looking for. A girl that will not have a problem enjoying their penis in sexual situations.
Not to say that non-op girls don't wish that they would have been born as a cis female, but (like myself) they would rather not risk a botched surgery (very low percentage of occurrence, but the risk is there) when they can derive pleasure from what they already have.
And being someone who is also attracted to a non-op trans girl. I know we are very few and far between.

As for those of you that are using the term "ladyboy". That is a direct translation from the thai work "kathoey". So every time someone on here says they like ladyboys. I think of a thai girl.
And for "shemale". That's a term used almost exclusively to describe a non-op (or even pre-op) transsexual porn actress. A lot of these porn actresses cycle their hormones in order to either sustain an erection or so they can have ejaculate that is white (or even passably both). There are girls out there that are able to ejaculate without cycling their hormones, but in most cases that just seminal fluid, no semen there to turn it white. And there are even some (like myself) who have stopped ejaculating all together. That's not to say these girls are unable to obtain a orgasm (or multiple ), just that there is no proof of it as is the case with most cis women who don't ejaculate.
I know there are some girls that don't do any kind of porn that don't mind being called this term at all. But than there are a lot more who do (I'm one that minds).
Terms like "ladyboy", "shemale", "dick-girl", "slut", "whore", so on and so forth are objectifying. But if that's what you guys are looking for... I'm sure there are girls out there willing to be your sex slave. But know that the majority of women (cis and trans) don't like to be objectified. So if your looking to pursue a relationship. I'd advise against using these terms unless the girl has said it was ok.

Now for all the ungendering I've seen in this post. Though the mods have already notified everybody in this thread of it already. I just thought I'd clarify it for you all.
A transsexual woman is a real girl and a gg (genetic girl). There was a study (in Sweden I believe) in the early noughties (that's 2000 to 2009 for those that don't know) where a sample of pre and post transition transsexual women (meaning before and after hormone treatment) cadavers to see if their brain chemistry and make up were similar or not to cis female brains. The study showed that they were in fact identical.
So it's been proven that transsexual women are truly female brained. So saying that they are not true or real women is a false misconception.

Now if your looking for a more accurate and less offensive way of labeling people. Add transgendered and cisgendered to your vocabularies.
The meaning of the two;
Transgendered: is a general term applied to a variety of individuals, behaviors, and groups involving tendencies to vary from culturally conventional gender roles. So transsexuals, cross-dressers, drag queens and kings, transvestites, gender-queer, bi-gender, and even some intersex people fit into that category. For more in depth explanation see http://en.wikipedia.org/wiki/Transgender
Cisgendered: is an adjective used in the context of gender issues and counselling to refer to a class of gender identities formed by a match between an individual's gender identity and the behavior or role considered appropriate for one's sex. For more in depth explanation see http://en.wikipedia.org/wiki/Cisgender

Hope I've expanded the minds of at least a few people.

I think castration is to broad of a word and is mainly referenced towards men (when the general public is concerned). Maybe we could refer to those girls as orchtified or orkie (Orchiectomy is the procedure of removing the testicles) trans girls. *shrug*
It's just that the word castration is such an ugly word in my opinion, and probably same for other girls.

Though I am curious of why you prefer a girl who has had their orkiectomy?