how big of a role does hardware play?
As in all things SQL Server, the answer is "it depends".  A good database developer can design an application to mitigate SQL Server hardware requirements with attention to detail on database design, index/query tuning, and application design (e.g. appropriate data caching).  So it seems you may have covered that part if you see index seeks rather than scans in the execution plans with the actual number of rows being the minimum needed.

Whether or not your hardware is up for the task will depends much on response time service level agreements (SLAs).  Doing the math at 30 users and twice a minute, the server will need to be able to execute 120 selects, 120 updates, and 60 updates a minute.  This comes to 5 queries per second, which my gut indicates can achieve sub-second response time on the PC class hardware you mentioned, especially if the entire database will fit in RAM (which is probably can based on your description) and you are accessing a small number of rows per query.