Ok you can mulch installs easily. Tools - wheelbarrow, pitchfork, large aluminum manure shovel (much bigger than normal shovel with short handle usually). spade shovel (for edging) and hard rake (for spreading mulch[or hand]).
Get your mulch from a nursery. Most if not all of them sell bulk mulch which is cheaper and more eco friendly than mulch in plastic bags. should cost around $20/$25. Usually delivery fee will be around $50. depending on your area and the specific site conditions charge between $50-$100 (or more possibly) per yard of mulch installed. I think mulch weighs around 800lb/ yard. fill dirt around 2000lb/yard.
Do mulch anytime. for people who think mulch draws termites, just tell them you keep it 2"-3" deep and keep it away from the house a few inches. tell them that ALL their neighbors have mulch.
depending if you need to do a major bed expansion you might need to rent a sod stripper or buy a manual one ($300 and hard work i probably wouldnt unless you use alot). otherwise if its manageable strip soil with a shovel or tiller.
for edging use the spade shovel and keep the edge of the bed very nice and defined.