The most useful pieces of scrap are chunks of L-stock (or angle iron, or whatever name you want to assign it). Short or long, they come in handy for getting weldments square and in plane to corresponding members like; square tubing frame members, tabs, gussets, you name it. Most steel and aluminum L-stock is pretty darn square and flat. If you want to do really nice work, or are thinking about investing in some steel dedicated to fixtures, then go with cold-rolled or cold-formed steel instead of hot-formed or hot-rolled steel. You can tell the difference because cold rolled has a much smoother surface, has sharper edges, is much more square/precise size, and generally has much less mill-scale. It's also much more expensive. Hot formed steel will do the trick for most applications, no problem :-) All different types of stock can be used for fixtures; plate, strip, round/square tubing, etc. L-stock is the most versatile.
Now that you know what to use, here's how to use it...
Make sure the scraps you are using to help make your weldments flat are flat themselves. Put a known straight edge like a ruller on it and make sure its not bent or twisted. Make sure you grind/file off any burrs; these will throw you off faster than... something really fast... If you can help it, clamp the tube/whatever to be welded through the cross-section of the fixture-piece. This way any incongruities are distributed across the face of the weldment, so nothing gets kicked-out (this is so hard to explain by typing it out...)
When you clamp it together, start off with your C-clamps lightly in place, or start with spring clamps and replace them with C-clamps once you've made your final adjustments and everything is exactly where you want it to be. In the pictures I have here, I'm using spring clamps where I could be using C-clamps, just because this was a low-budget, low-precision application; but the method can be used to get spaceship results!
Don't get in a rush to take the clamps off. Let the welds cool off a bit before so things don't move around on you from the thermal expansion/contraction.
Find a TechShop in your area by going to www.techshop.com. They have tons of great metal working tools, MIG and TIG welders and all sorts of goodies for everyone, for way cheaper than trying to buy them for yourself.
Below are some pictures of examples of these methods being put to use to modify a service cart of mine.
Hope you all enjoy, and comment below if you have questions/comments on the subject!