For the record, "Messianic Judaism" is not considered to be actually Jewish by any major branch of Judaism. It's a movement that grew our of Christianity rather than of Judaism, and is considered rather insidious by many Jewish people.
As yoch_wint says, you do really need to live close to a synagogue in order to convert: being Jewish is about practice more than anything, and that practice is done as part of a community. Any kind of conversion also must happen with the support and guidance of a rabbi, who will be attached to a synagogue. Conversion usually takes between one and three years: at least one because you need to get the feel of a Jewish year, the rhythmn of the festivals etc. It's only after you have been under the guidance of a rabbi for this time, been assessed by a beit din (a groupd of three rabbis, usually including your sponsoring rabbi, who see if you're ready to become Jewish), and have come out of the mikveh that you become Jewish legally speaking--ie that you could identify as Jewish on forms and things. In order to make aliyah (return to Israel as a Jewish person), the beit din would have to be Orthodox.
Reform/Conservative/Liberal/Orthodox differ primarily on their answers to the question: what is Torah? And then differences in mitzvot follow from there--to liberal branches, torah is usually seen as a continually developing human creation inspired by G?d, whereas for Orthodox branches it's seen as G?d's Law as given to Moses, and therefore their approaches to halakha are different. This does not mean that liberal Jewish people are inherently more lax than orthodox ones, nor that orthodox judaism is inherently less suited for our time. It's about what connects best with you and your understanding of torah (which you may well not know much about yet!), and the communities you are most comfortable with.
If you don't live near a synagogue now, you can focus on learning about Judaism--there are a lot of resources out there, like myjewishlearning, chabad, jewishfaq, as well as holy texts being available for free with English translations on Sefaria (also an app!). You could look into learning Hebrew, even. There are also probably PDFs to be found of books like Anita Diamant's Choosing a Jewish Life, which is about her conversion (which is liberal--either Reform or Conservative, I'm not sure?), and you could check out books about jewish topics at bookshops near you or on amazon.
(Also, you could look into Jewish opinions on Jesus (Joshua), if you like. He obviously isn't considered the Messiah by Jewish people, and he isn't always considered good--much of what he does feels quite disrespectful (causing destruction when he knocks over the tables of the money-lenders, for example). Opinions are mixed! You might find that interesting as someone raised catholic, at least culturally speaking, if not religiously so. And Jesus is obviously a complicated subject for Jewish people considering the long history of Christian antisemitism.)