Do you own a welder? Or have access to one? A good one is expensive, you know...
MIG welding is the easiest to learn. Basically, you point the gun at the part and pull the trigger. That said, you'll need some practice before you can do it correctly. For something like this, you can probably get by with tack welds which won't require much skill. If your metal is thin, I would definitely worry about it warping! If you have a thick piece of copper or aluminum and can place it under the piece being welded, it will draw some of the heat away and reduce the risk of warping. I would think that the biggest problem you'd have with a MIG welder is keeping the pieces in place. If you just rest the bolts on the plate, the wire coming out of the gun will knock them out of place! Also, keep in mind that a standard MIG setup only works with mild steel. Stainless steel and aluminum can be done, but they require special supplies and equipment.
If I were to do this, I'd probably use my TIG welder rather than the MIG. It gives much better control control over the weld. It's also somewhat difficult to learn. BTW, have you considered soldering? I only know welding, but wonder if soldering might not be cheaper, easier, and give you all the strength you require...