I try to start with the best possible components that I can find, especially brass. I tend to buy Lapua if it's available in the cartridge I want. I just feel like having great brass and bullets will help me from second guessing myself during load development.
If it's a somewhat common cartridge, I'll reference the reloading manuals to see what they think is the accurate loading for the bullet weight I want. Then I will do some Googling with that bullet weight along with the powder the manual suggests and see what other people are claiming their accurate load to be. A lot of times people's accurate loads they post are pretty darn close to what the manual says also. I'll make an educated guess based on the reloading manuals and the Internet's opinions.
For example, the reloading manual says for ABC bullet use 56grains of XYZ powder. People on the Internet claim they have found accuracy anywhere from 55-58grains with the same bullet/powder combo. Since both the manual the Internet opinions seem to jive together, my testing window powder spread is only 3 grains instead of the entire Minimum to Maximum charges.
So far this has seemed to work great to find the accuracy node for a particular bullet/powder combo.
I will measure my COAL and take note of it. But I will load my initial testing rounds as long as they can possibly be and still be magazine fed. To the point they barely fit in the mag. Sometimes I get lucky and these shoot great right away. Other times it takes a bit more work to dial in the seating depth. (I start this way because I would prefer to magazine feed my rifles. That's why they have magazines...)
First of all, always remember to not start gathering grouping data until your barrel is seasoned. Shoot a handful of rounds to get some copper in the barrel to bring it up in temp some.
I don't round robin or single feed usually. I see the merit in the round robin method and understand the benefits. However, just for myself I have found that I shoot much better groups if I don't physically move anymore than needed. Once I get my rifle settled and my cheek gets onto the stock I try to shoot 5 in a row (or however many you want your groups to be). This just seems like it produces the best results for me.
From those groups, I'll take the best 2 normally (sometimes 3) and load more to test over a chrono for ES/SD. Whatever loading had the small group with the small ES/SD will become my load.
There have been some bullets that after much testing just plain didn't shoot well in the rifle that I really wanted to shoot them in. It's hard to put my ego aside, but I have had to "give up" on certain bullets. Then, what do you know, another bullet seems to shoot great with almost any powder charge I give to it in that same rifle.
One thing is for sure. I haven't saved money by reloading. All of a sudden when you realize how much control you have over the accuracy of your firearm, you can no longer be happy with 1 inch groups! So I end up testing and testing until all of those holes are touching! (And for me, 3 shots isn't a group).
And the most important part that you cannot forget! You save your best targets, write the load data on them, and show them to everyone you know... Especially your shooting buddies that don't reload.