Ok, the only thing I've every arc welded was some cast iron which is quite hard to do. But yes remove the slag before welding over the top again. Assuming you are welding the edge of two plate together always grind a 45 degree chamfer probably about halfway into both plates before welding, then fill the gap. This way if you grind the weld down after to tidy up it will still be strong without you grinding all the strength off. With practise you will get to the point where you won't need a grinder, well thats the theory I will yet you know when I get there. I will be the first to say I can't weld very well so your probably better off listening to someone else anyway.

When we first started building Turb years ago we arc'd the lower chassis, before getting a MIG which was better. Personally i've done more TIG so thats what Im best at, experience says just practice and you will get better.