re: Can I get advice/tips for my lawn after the winter? ::Updated with pics:::

Your primary grass in that picture is St. Augustine. It's known as carpet grass, the other grasses are winter weeds, stickers, etc. Broadcast spreading the 13-13-13 and pelletized lime in late March will do the trick. That St Aug will grow quick and thick, choking out the other weeds. You may have to mow twice a week for a few weeks. lol A trick with St Aug, is when you get into the hotter months of July and August don't cut it very low.