When I can, I make my first cuts length of fabric instead of width of fabric because I feel that then I will have st least two edges that will be straight of grain .

I do cut a really long piece of fabric onto a manageable length before I start cutting my lengthwise strips

Some stores will rip fabric to get the straight line this distorts the edge and is not a good idea. You can line up fabric to cut off by; hold fabric up with one selvedge at. The top. Lift up the second selvedge take no notice of the centre fold. Keep sliding the selvedges along the top( keeping together) until the fold is square. Now lay down and gently cut level.
Some fabric has a terrible waste. Cutting across your way may alter the joining of some blocks. One direction has more stretch than the other, not sure which is which.sorry.

I've been taught how to stretch fabric, corner to corner to bring it back as far as possible into square. On the other hand, if I am starting with a large piece of fabric,longer than 42 inches, I tend to cut what I need from the length side, saving the longest piece possible for future sashings or borders. I have no idea if that causes problems later on in the quilt.

I also try to plan my cuts using the lengthwise grains to cut my borders first or save that area for cutting the borders later. I like to cut other pieces on that grain too. It sews so much better - no stretch.
Pat

The width of the fabric has more stretch. As far as sewing seams in rectangles or squares, you'll have two sides WOF and two sides LOF. If you're worried about stretch on certain sides of a block, you can plan out your cutting. I, personally, don't worry about it.... except for blocks that are cut on the bias. Usually, on a block with bias edges, you'd like to have those edges on the straight of grain.

I always try to cut my log cabin blocks on LOF. I picked that up from Judy Martin, the queen of log cabin makers. It really does make a difference.

I'm a LOF most the time and for sure my borders.

On a large piece of fabric, after heavy starching, I make my first cut LOF and start
cutting from the fold. My first cut I add a smidge then trim after cutting the fold.
That's my own technique and I'm happy with it.

I agree with Tartan with cutting the border. Also if it happens to be a directional print. I think it looks much nicer. Interesting comment made by Dunster of what Judy Martin suggest.