ABSOLUTE Necessities?

I would buy the filter first.

Really it doesn't matter the order in which they are bought in my opinion, as it is likely you wont be adding any fish until you have all of them and have it cycled. I suppose filter if you had to choose one.

def. filter and heater, in that order. Does the tank include lighting? If not get a light before you get plants.

Alright so your lighting depends on what plants you want. That is a good deal

i'd say for sure filter first so you can start cycling the tank, since it takes a few weeks.

I would spend it on lighting.

comprehensive liquid test kit. you can print out a page to one for cheap online and try to get a store to price match.

You can pick up a new 24" 250 DE HQI metal halide setup for 100 bucks on ebay. I just nabbed one for my planted tanks. It is still than one Geissmann MH HQI DE light bulb. However that would mean you need to buy Co2 system.

If I were you, I would pick up at least a dual strip T-5 fixture for 50$ or a dual Compact flourscent fixture for $75. Just got the prices of ebay. You really don't need CO2 with either T5 or CF's. You will still get good growth, and healthy plants.

Substrate? I would get a bottle of Sea Chem Flourish, and Sea chem root tabs.
Filter? Depending on the bioload, you could get away with a $10 powerhead,
Heater? no side stepping those

For 65-100 bucks you could have a nice tank. The main thing is lighting, proper ferts, and maintence.