Yes, RSLinx handles the communications between the PLC and your PC. The basic version is a free download from Rockwell's site.
RSLogix is where you do the actual programming. Traditionally you would need RSLogix 500 Starter to program the Micrologix 1200 (p/n 9324-RL0100ENE) which retails for about $600. However, they recently released a version called "RSLogix Micro" which appears to be identical to Starter but with no SLC support (p/n 9324-RLM0100ENE). If you can get in touch with your distributor be sure to ask about this as it would probably save you some $$$.