Hi Alexander,

What you build first will depend on your experience (and that of your grandfather). If in doubt then build a simple one first. Good quality radio gear, batteries and speed controllers can be recycled into a more complex bot as you gain experience.
I suggest you have a look at the live events section and find the next one that is within traveling distance of you. Build yourself a simple bot (drill motor/gearboxes, no weapon), sign up as a roboteer and go and compete. There is nothing that beats being in the pits as a way to see how everyone else has solved the problems of building a fighting robot. And there are few experiences that match the buzz of driving your own robot in an arena full of others, with everyone trying to win.
A simple bot can be built in a couple of weeks. Drill motor/gearboxes are good because they are inexpensive and widely available and only need wheels to make an effective power unit. Lots of people on the forum will be glad to tell you how to get the chucks off and wheels that screw directly onto the 3/8 UNF thread exposed by removing the chuck can be bought for about £8 - 10 each. You can make the body out of anything - wood is good because it is cheap and easy to work. Ive seen one where the maker used the plastic case that the one of the drills had come in as combined mounting frame and armour.
I hope to see you at a live event soon.