I've hesitated in posting this, sometimes I feel like I should keep my big mouth shut, but...what the heck, here goes:
If you're interested in practicing Vajrayana Buddhism, the most important consideration is who your teacher will be.
You do not need to be a monk to practice Vajrayana. In fact, as a Western person, I strongly recommend you check out teachers, centers, and various traditions, and decide who your teacher will be, before you consider monastic ordination. This will usually mean that you then will affiliate yourself, more or less, with that teacher's lineage, or center, or both.
Once that is clear, and you have a working foundation and a practice, you can consider whether monasticism is something you wish to pursue. This sort of undertaking, IMO, should be discussed with one's personal teacher. Then, and only then, would one consider affiliating oneself with a monastery. There are hundreds of monasteries representing various Tibetan traditions--and those that are affiliated with our lineage and practice will naturally be a better fit for you. I also consider these affiliations when choosing where to send my money...but for me, it's somewhat easier as I have relatives in several monasteries, so it's an easy choice who I support.
Now, if you are primarily interested in taking Monks' vows, and not in practicing Vajrayana, perhaps it doesn't matter so much where you go.
I don't want to discourage anyone from the earnest and noble aspiration to become a monk, which is why I hesitated to say a thing....but I felt these words would serve you on your path.
May any merit generated by on-line discussion
Be dedicated to the Ultimate Benefit of All Sentient Beings.