An easy one to start with then
Note: plants do have a circulatory system, its just different to animals, esp mammals. They draw water into the roots and this goes into long tubes all the way up to the leaves where it evaporates. As water evaporates it draws more up the tube by surface tension and capillary action, kind of like drinking a straw. As the water moves, nutients such as minerals are brought with it from the soil up to the leaves. Theres another system which goes the other way, but im not sure how that works.
The reason you need a cirulatory system is because of surface area/volume ratio. Above a certain distince from the outside the cells of the organsim cannot get to oxygen/food at a fast enough rate. This is the reason you dont have worms above about 1/2 cm wide, they get longer because that keeps the distance the same. You could have a worm 10 miles long, as long as it is no more than the critical width.
One way to get around this is to put air tubes reaching from the outside inwards. Then as long as no cell is too far from a tube, its OK. But they can ony be a certain length before diffusion doesnt work.
So the bottom of the tubes is filled with a liquid, many chemicals will disolve in water better than in air.
Something that can carry oxygen/co2 in it (heamoglobin like).
The ends could seal over with cells that can move the required stuff from the air into the liquid in the tubes.
The tubes could join up within the organism so that they can exchange liquid. However, its still moving by diffusion.
It could be pumped by the walls of the tubes contracting, like your throat when you swallow.
The same liquid could also carry nutrients, waste, hormone, anything that need to get to all of the cells.
Some of the cells in the middle of the tube network become better at pumping, so that those at the outside can become specialised into transfereing nutrients/gases into the liquid.
Voila, you have a proto-heart, a proto-blood, and proto-blood vessels.
Remember, at all stages it only has to compete with the previous stage. This is also not orthodox theory, this is just off the top of my head. It probably has several holes in it, but im sure they can be fixed.
Evidence:
Insects have air tubes going into their bodies.
I dont think fish have a heart (cos i know the gills evolved into it).
Plants dont need a pump to move water.
Many small organisms are just filled with water(n stuff).
In an embryo, the heart doesnt start beating for some time. Gets nutrients from amniotic fluid)
There are many liquid containing orifices, the mouth for example.
Arteries are partially contractile and muscle lined.
Next!