Hi Lana, The two bits approach is the way to cut this kind of slot, and cutting with a one pass type bit in MDF will burn up almost any bit PDQ. MDF is really just sawdust formed with glue into what passes for a sheet of wood. It is weak, hard to glue and finish, and the sawdust will ruin your lungs in a hurry. The one use for it is to make the second layer of a table you want to be flat. But there are other, better ways to make a plywood table top stay flat. There aren't many MDF fans here.
I have some old MDF scraps I keep around to push things through the router. When the bit exits the good piece, it drives into the MDF, which basically eliminates tearout on the back side of the good wood piece. MDF is cheap and expendable for this purpose.
A 1hp router is not particularly powerful so you feed rate has to really slow down. You don't want to be pushing the router forward against resistance, particularly in MDF. Generally bargain priced tools don't hold up very well. For a starter router, give the Bosch 1617 EVSPK kit, which includes both the fixed and plunge base and a half and quarter inch collets. CPO tools often has refurbished units that have a great reputation here. This kit used to go on sale for about $200. The fixed base can be used to mount the router in a table, and there's even a "key" you can get to adjust the height from above the table. There are lots of entries you can search for on how to make a basic router table without spending very much. A table mounted router is far safer than one used freehand.
I think Stick will come along shortly with a batch of pdf files with safety and user information galore. Download and read them is my personal recommendation.
Routers are one of the most useful tools you can have, right next to a decent table saw.
The more I do, the less I accomplish.