I recommend visiting the parishes closest to you and getting a feel for each one. For example, there's a Greek church, an OCA church, and a ROCOR cathedral near me. Though I love Greek chant and speak Russian, I will convert through the OCA church. It's closest, not as overwhelmingly large, and the priest not so busy that I feel like I'm imposing on him. Plus, my husband, who is supportive but has no immediate plans to convert, is not good with foreign languages. So basically, there's no one jurisdiction that's best for converts.
As for becoming a catechumen, some churches have a very rigorous program. The two I've inquired at have had me read some introductory books and attend a few discussions before telling me that I can be chrismated whenever I feel ready. Ironically, I would prefer more structure and this is, I think, a big part of why I have not converted yet.