first of all it is dependent of what operating system are you running on mainframe. On System z for operating systems zOS, zVSE and zVM you need to have DB2 Connect product. If you are using Linux on System z (like our company) there is no need for DB2 Connect product.
There are two Connect products. Connect Personal Edition and Connect Enterprise Edition. For Personal Edition only local computers can connect to mainframe. For Enterprise Edition also remote computers can connect to mainframe - so you have some kind of gateway. If using multiple connection to mainframe I suggest you to buy Connect Enterprise Edition.