Do a search for Benedictine Order and you will come up with what you are looking for I hope. They do have Oblates aswell for men who want to live in the community. Local to me, in England there is a Benedictine Monestary that men and women can become members off regardless of their age and health and financial situations etc because they are called Companions. They are not so tied as Oblates are. I did try looking but I need my own prayer to be as simple as possible and found it too much though would have loved to have gone through it I think. I could become a friend of the Monestary instead but I don’t know as really have only discovered my way with God this year and still enjoying this way though have been so for 25 years or so. I just wanted that extra belonging. I also looked at the Third Order and again I had typed that in search. But between the two whilst the Monestary is slightly harder to get to, if I did go any route I personally prefer the Benedictine order and choose Companion or even friend off. There is a place for everyone, the literature says so. I sadly, ran away next day or as good as ran away in that I sneaked back home as was too much for me. Luckily I an understanding priest who I can talk things through with him so I know what personally happend for me and yes I get that tug but also that tug for freedom with God too having only just found this style this year.
I hope it goes well for you and I would suggest just putting in Benedictine Order in the search engine and various monestaries etc may come up for you. Also speak with your priest who be hopefully, happy to help guide you through and you may discover that actually he could be an Oblate with the Benedictine Order - ours is. And if he is he will be able to really help guide you through that stages. Its about three years to become an Oblate and the same if you are thinking of permiment residence as a Monk. There could be a Monestary not that far from you and you can go and stay there and find out more of their lives etc. Again do a search on the the web and ask your Priest.
God Bless You