Multiple accesses to a table

Hi all, 
I'm looking for practical examples on how to solve a problem of concurrent accesses in the following scenario. 

I have N clients accessing the same table and performing the sequence of operations: 
1. read M Records 
2. process and delete the M records 

During these operations, each client should block only the M rows and not the entire table to avoid slowing down other clients. 

Thanks in advance for any help.