Your most important number, when figuring our whether this will be profitable is your production rate. You need to know how many board feet per day you will be able to produce. That is what limit your profits, so that is what you need to figure out first.
Once you know that, you will know how many boards you will have at the end of the week, and you can figure out your net income from selling them at the rate your buyer will buy them.
Knowing how much you can make, you can then figure out how much your expenses will be. Logs are a cost. So are bands. So is fuel. And your time is a cost (although you may not think so yet, but you will need to be paid). Another cost is insurance. Others have mentioned the costs of equipment (This is an up-front cost or "initial investment" that allows you to be in business, but you should recover that cost over time... so it should figure into your calculations of profit).
Once you know what your production rate is (bf/hour) you can multiply that by how many hours per day you want to work. Say your production rate is 100 bf/hour. In an 8 hour day you can produce 800 bf. (I use this because this is roughly what my sawmill can produce when I am fully up to speed, and there are no mechanical failures, and I have logs ready, and bands sharpened, and fuel available, and space to put the lumber... that is.... ALL of that is set up PERFECT). Now, if you produce 800 bf in a day, and all of it is perfectly sellable to the fencing customer, and you sell that at .75/bf (use the lower number to be conservative)... you can pull in $600 in a day maybe 2400 / week if you saw 4 days a week.
Now subtract off your cost of logs.... 800 bf of logs will cost you about $200. I suppose white oak is readily available where you are, but that is not always going to be the cost of white oak logs. Just consider that. For a 4 day week, you'll need 800 worth of logs.
Now subtract off your fuel. 8 hours of sawing costs me about 10 gallons of fuel at 2 bucks a gallon so 20 bucks a day, or 80 bucks a 4-day week. Gas is cheap now, but won't always be so consider what happens when gas goes back to 4 bucks a gallon.
Now subtract off your cost for bands. 8 hours of sawing uses 4 sharp bands, which cost me about 100 for new, or about 50 if I resharpen. Bands are no good when they are dull, so you must keep them sharp. Either you will pay someone to sharpen them, or you will need to buy a sharpener (so add to your capital equipment cost). Figure about 200 for bands a week.
Now subtract off your costs for "Parts". A fellow sawyer says... "got a mill... you will need a welder". You need new belts, new hydraulic hoses, new carburetor, new spark plugs, new roller bearings, new zip ties, new jack stands, new bushings, new bolts and washers.... a sawmill EATS parts. This expense is hard to estimate, but from tracking this over time, my sawmill needs about 50 dollars of parts a week or so. (A $300 carb, for example, kept me running for about 6 weeks before the next thing broke).
If you have to "pay" anything else, you should add that up. If you have to pay for a helper to off-bear lumber, for example, how much a week do you pay? You may be able give slabs away, but you may have to drop them off yourself. The time you spend on that costs you money (and gas, and maybe a busted tail-light too).
Now... add up all those costs .... make sure they are of the same "timeframe": Dollars / week for example.
Subtract that from your 2400 you can make in a day. That's your profit margin.
Now, can you pay your rent, buy food for you and the family, make the car payment, health insurance, real estate taxes, tuition fees, and set a little aside for retirement? Only you can determine that, but be sure to figure it in.
Now, remember that 800 bf/day number. I got that rate of production after running my sawmill for 2 years and learning what I should do and what I should NOT do. I also took classes on forestry, log and lumber grading. I spend weeks watching how other sawyers do their thing. Also, learning about my sawmill, how to do things. How to repair it when I break it. Where to get parts. Where to get bands sharpened. You will need time to figure all of these things out. (Can you afford not to eat while you are doing those things).
You will not get 800 bf / day when you start. You may get 200 of usable lumber the first time you try and you might give up at that point. But you will work up to 800 bf/day, if you stick with it. But it may take a year or more before you get there.
You are definitely asking the right questions though.... keep at it....
Eric Steadle