Navigate on cycle recruiting

Hi all, 

I am looking for some guidance on the current job market and how to navigate the recruiting process. First a brief

Introduction about myself: 
23 y.o with a Bachelor in economics  from Bocconi (3.7) with exchange semester at NYU Stern (3.9). 2 SA position in PE shops in italy during the bachelor and currently interning since december at a PE shop in NYC. I got the FT offer but lost the H1B lottery ( I am on J1 currently ). My long term goal would be to become a PM at a l/s HF in NYC.

Current situation : 

As I knew that the H1 was a gable I also applied to the only MSF in the city which offered 3 years opt and required no GMAT ie : Fordham. I got a full scholarship and currently I see this as the only practical option to remain in NYC. 

Where I need help :

Firstly If you guys could give me some feddbacks of how Fordham is seen on the streets and if it closes many doors a-piori. Secondly, the main reason why I am writing this post, I intend to finish this MSF in 1 year meaning I would finish in August 2025, however I noticed that many firsm intake SA before, should i prolongue tha master to account for an internhsip in the summer of 2025 ? Do I have a shot at buyside due to my experience of 1 year in PE ? Should I only target IB ? Should I apply to SA positions or is it better to pply for FT ? and more generally how's the on cycle recruiting process for MS students, does it change from undergraduate or is it mostly the same ? 

Many thanks for any help ,