A few years ago, I started using Handwriting Without Tears for our handwriting curriculum. I realized last year, though, that Handwriting Without Tears is really focused on public schools, not homeschoolers. I wouldn't say they are unfriendly to homeschoolers (many homeschoolers use the program), but I wouldn't say they are exactly friendly either. They are focusing their marketing and curriculum efforts primarily on equipping classroom teachers. So, I haven't really wanted to purchase more workbooks from them. I suppose that sounds silly. In any case, I have my kids practice their handwriting each day during grades K-4. In third grade, I do have my kids learn how to write in cursive. I enjoy it and I think that it is beautiful. I think kids learn a lot from practicing cursive. It is often easier to write quickly than manuscript.
I have found several great free printing and cursive websites that I am using, am going to use in the future, and have already used. After my children have practiced the letters singularly, I am going to write a list of 4-8 words on large lined paper for them to copy 3 times each. Another exercise is for them copy words out of a beginning picture dictionary and make their own picture dictionary. One more idea is for my child to find their favorite picture book and copy it one sentence at a time as copywork/handwriting practice. My daughter Sami loves to do this just because she wants to.
In terms of what letters to introduce first, kidzone groups the lowercase cursive letters into similar shaped letters. I am going to follow this plan with Sami next year. Handwriting without Tears lists their order HERE if you'd like to use other worksheets and follow their order. With printing, I've found that most printing worksheets go from A to Z.