Years ago I did some "Standard" Contracts for ASGCA, based on AIA language, modified for golf. It was a member service idea, and some guys use them, some ignore them, some modify them, and most have their own pet clauses that they add to personalize it based on their experience. There really is no standard.
There were long and short form for full designs, and one for master plans and preliminary planning services, which was only 3-4 pages. No doubt the smaller the project, the smaller the agreement needs to be. That standard agreement covers the basic things like Ken Mouns, which I think is a pretty good model.
I once sent my little three page letter agreement to my attorney, and it came back at six pages, so if you are familiar with AIA type contracts, and know what you are contracting for, I suggest its better just to write your own.
In general, I think most archies try for simplicity, until the run into a problem client, and then having something like Ken's helps. A letter really doesn't cover things you think would be understood, like the fact that you are an independent contractor, or who owns the plans, ideas, etc. If the owner owns them, then I like to have a clause that he can't use them for other projects, or without further supervision by me.
Case in point, years ago an ASGCA architect did a master plan. Showed a green over a pond with a retaining wall. later, they hired another gca, but liked the concept. When the wall they built to another final plan, and built in house without engineering, who do you think they sued? Yeah, the ASGCA guy who never designed the wall in that was going to be built.
As to payment schedules, you always get 10-33% upfront, the more the better. For consulting, you generally just bill once a month based on hours spent, expenses, etc. If you are to produce some actual plans or work product, then billing tends to follow completion, although partial payments are typical, too.