I press each round as I go, to make sure that my seams are completely pressed. I have a TV tray set up next to me with my little travel ironing mat and mini iron. Isn't is cute? It's pink too! LOL (PS...I tried to find a link for it, but couldn't find the same one. I bought mine at a National Quilt Show from a vendor.)
I have a CLOSET full of beautiful fabric, yet I seem drawn to those little bits of fabric that others throw away! I guess that's where that FRUGAL part of me comes in. I don't like to see waste. I'm done with the Scrappy Diamonds for the moment, I have bins of big strips for my Heartstrings blocks and now any bright colored fabric that comes along that is 1" wide, I snag for my little log cabins. I originally saw this on Melly and Me's blog--as blocks. When I went back to get the link for you, they now have a Scrappy Log Cabin challenge and a tutorial. They do their's by foundation piecing and I'm doing mine a bit different, although I did use their size strips.
I'm not paying any attention to lights/darks or whatever. I'm just putting them on as I pull them out of my little drawers. I found that if I pre-cut the strips into the sizes of 'logs' that I need, I'm more prone to sew on them when I have a few minutes. I got these little drawers and labeled them with the size. I needed one more drawer, so I used a little basket for the 2 1/2" squares for the center and the 2 1/2" logs for the 1st round. I found I can make 2 log cabins in 15 minutes. I much prefer pre-cutting the logs because I have found that you can keep your log cabin 'square' easier. Otherwise you are always having to trim and square it up. If your log FITS your square as you are sewing it on, then you know you are okay. If it doesn't, then you need to check your seam allowances. I've tried paper piecing log cabins, and find them too tedious. I've also tried doing them by laying down the strips and adding the log cabins that way (similar to the Mile a Minute blocks). But you still have to trim them apart. In the way I do them, I can just cut a few logs as I am cleaning up a mess on my table or find a few scraps.