To create perfect round dots you need some tools! Check out Trademe for "mandala tools" - there are lots of options. Whitcoulls stocks mini rock art kits and these are a great way to get started. You can also make do with items you have at home such as tooth picks and chop sticks. If all else fails - just go out into the garden and search for some suitable sticks!
You can use any acrylic paint on stones, however the higher quality paint will give better coverage and be more vibrant. Warehouse Stationery have a great selection of acrylic paints. Another option is to visit your local Resene Colour Shop. Test pots are only $6 each and a little goes a long way. The Resene metallics and special effects paint is ammmaaazzing!
It's really important to protect your rocks with UV resistant sealer as this will prevent the paint from flaking and peeling off. A good option is "Rust-oleum" from Mitre10. The clear gloss is a lovely finish and it will ensure your painted rocks can survive all weather conditions.
If you're looking for design ideas, check out Pinterest and artists such as Elspeth McLean and Mandala Stone Art. While it's great to look for inspiration, don't get too hung up on comparing your rocks to other peoples - it's all about just enjoying the process and having fun! Rock painting is fabulous "therapy" for people of all ages!