I use the big plexi base you are talking about, with a small laminate trimmer type router. My base was made by Terry "Visteonguy," look at his posts about signs, there are photos there of his base.
You can use a small v bit. The best way to make sure the router stays where you want it is to have a clamped piece of wood beside the router base so that it cannot move. For example if you are doing letters, than many will have vertical parts and horizontal parts. You clamp your scrap of wood the proper distance from the bit so that when you run your router in a straight line, it follows the edge of the scrap wood. Of course you need to practise first!
If this isn't clear, write again and I'll try and explain better.