DIY Drip Irrigation, vertical cage style. Need input on pump size

Alright, so I'm drafting up plans for a new flower cab build, as I'm deeming mine as too inefficient. I'll give you a basic idea of what the cage will be like, it will be an octagonal shape with a vertical light in the center, the cage will be constructed out of 3/4" pvc pipe, with 8 sites per level, and 4 levels spaced about 10" apart. The sites will be staggered, so if they grow to the higher level, they will have space, giving them a total of about 20" of space. This will be a SOG style grow so they shouldn't get too big.

I'm going to have a total of 32 sites, each site has its own pot and I will be using soil at first, but transferring into a soilless medium / hempy setup in the future. On top of this I'm building a drip irrigation setup that I will run on a timer as the plants need it. I want to have a central res with a submersible pump, feeding a 4 outlet drip manifold. I'll be running 1/4" line and fittings, and the manifold will disperse a line to each level on the system. Each level will be a circular shape with inline drip heads installed.

From what I've gathered, the drippers work best at 15-20psi and have a flow rate of .5gph. Each head on the manifold flows on average at 6gph, which I feel will be sufficient.

The part I'm not sure of is how large of a pump would be best suited for this kind of setup? The pump will be on the floor, and will need to pump to the top of the cage where the manifold will be installed, then the drip lines will lead to each level from there. The total height will be around 4'. I only plan on running the system for 15 mins a day, maybe giving them a day in between runs. 15 mins should flow half a liter to each dripper, which will definitely soak them.

What size pump would you guys think of going with?
 
to summarize, the drippers need 15-20psi to flow the .5gph. there will be 4 circle drip rings, each line coming from the manifold will be around 18 feet long, and each have 8 drippers.

So the water path will be as follows:

pump output is 1/2", 2-4' up to manifold. Manifold has 4 1/4" outputs which the line will be attached to. Each line will have a T fitting adding up to 18' long in a closed loop with 8 drippers per line.

The total amount of line that will be used is around 72 feet @ 1/4". the pump output will be 2-4' @ 1/2".

I'm thinking that a 300gph would be good enough for the system. I've never calculated this stuff before though so I may be off.
 
medium doesn't matter, I'm just trying to size a pump to provide enough pressure for the system. The medium will be changing, soil, hempy, whatever strikes my mood.
 
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