OK, so you are on your way
The 600w is a good light but it does put out quite a bit of heat. you will have to make a way to remove the heat and bring in fresh air. You say it is staying 80f during the day with the floros, with the HID it will get warmer.
You said your flowering space is 144 square feet??? That is a very big space for flowering. I am assuming that you are using a spare room or something similar? What you will need to do is get some 4x8 sheets of the silverbacked insulation board that is at least 3/4" thick so that you can build a walled off area that is reflective so that you can get the most usage out of your lighting. Light tends to spread out in all directions and a good bit of it will be lost without having reflective walls surrounding your flowering area. You have a choice; you can either build a complete flower room that is an enclosed environment that is light tight or you can just enclose half way up to trap most of your light, but then the whole room will have to be light tight and maintain strong light discipline as you must not have any light intrusion into the flowering space during the lights out period.
It is also imperative that you make a way to cool the air within the grow space and refresh it with outside air or supply some way of recycling the CO2 within the space. Most of us here have fully enclosed flowering spaces with centrifugal type exaust fans that pull the air out of the space which then pulls fresh air in from outside so that it is refreshed with co2.
One key with the amount of light versus how tall you grow before switching to flowering; the bigger the plants get before flowering, the more space you will need, the more lighting you will need. The 1 600w will cover a 4'x4' well and give good bud growth. However, if you have a bunch of plants that you want to get the most from, then you will want to let them get about 12-18" tall before flowering(generally speaking as different plants will stretch different amounts). This will require more lighting to properly cover the space and give good bud growth. Technically you could flower them from starting right out of the ground but you will not get the amount of bud that you would get if you veg them long enough for the plants to mature some. When you put them into flowering is really up to you and how you decide to grow them
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