Yes, it would be possible to setup a reeftank for under $350.00. This, as you already meantioned, would get you the bare essentials but nothing else. Here's a quick list below:
12 gallon Eclipse Aquarium :$150.00
---Includes some Filtration (Carbon, Sponge and Pad) and Lighting
15lbs Livesand: $15.00
15lbs Liverock: $30.00
Extra Maxi-Jet Powerhead: $15.00
Test Kits:
Nitrate: $10.00
Nitrite: $10.00
Ammonia: $10.00
pH: 10.00
Hydrometer: $7.00
Heater: $15.00
Thermometer: $2.00
Salt Mix: $20.00
Having all of the above add up to only $284...Priceless!
The total cost for the above would be $284 which would give you some extra money to upgrade the lighting system on the tank to some power compacts. You should be under $350.00 when the lighting is completed.
But my question is why would you want to be so cheap with an aquarium? Sure, it can be done, but why? What I explained above was merely just the items that needed to be listed. I'm not even going to go into the cost of water changes, cooling, fans, a sump, a skimmer, additives, the monthly cost of electricity, fish, corals, fish food, etc. If you're serious about getting into a reef aquarium, save up enough to be able to purchase quality equipment which will last you for years.
On a side note, my electricity bill alone is around $220.00 per month not including the water bill for the RO/DI...I'm almost afraid to look at that
Graham