@Christian Smith
While of course you should seek advice from professional attorney and CPA, it all sort of depends... Lets look at each separately...
For your renovation work, you can't really "just split the profits." One of you is getting a check written to your name or company name (I assume if you are during pure cash whats the point of asking...). Only if somehow you had your clients write each of you a check, then the two of you are running individual businesses. So, if one person receives a check, then the first person would have to pay the other somehow. Is that a salary? Or as a independent contractor? Do you see where this is going? In case of an audit, you need to have a paper trail. Also, what is your locality's requirements for contractors for commercial liability and workmen's comp insurances?
So, this leads to a company of some sort, be it LLC taxed as a whatever (partnership, S Corp, C Corp) or perhaps a partnership. I don't know what your local requirements are for costs incurred/required for setting each type of company nor the related costs to maintaining and doing the tax filings (e.g. do you do your own accounting and taxes? Would you really keep wanting to?) Also, what sort of liability are you trying to protect yourself against? i.e. is a potentially more complicated/costly business structure necessary to protect you when, perhaps, you don't have that much to protect.
For flipping, if you search around you can find info about how a LLC taxed as a C-Corp would be a preferred structure for tax and asset protection. Again, how much complexity can you endure, and is it worth it? Remember, for the incorporated entities (and I think even partnerships maybe) you are going to need a separate bank account and operate WITHOUT co-mingling your personnal and business funds. If you do, you have "pierced the corporate veil" and thus negated your asset protection afforded by the business entity (thus, what was the point?)?
In short, for your construction work, figure out your overhead costs and determine what sort of risk you are willing to accept. Then, determine what business structure you want to mitigate the risk. Also, you can always create a company or change your company later. Not necessarily the best idea, but maybe after you get started, get a tax return done, then you can see where and how you want to go.
For your flipping, you really probably should have some sort of written agreement between the two of you on how you will operate (I hope you've at least thought it all through). That pretty forms a partnership. So, probably best to do a multi-member LLC for the asset protection. Partnerships generate K-1 forms for your tax returns so the reporting of income is set.
I hope this overview helps. I can't get into too much detail as unless you are in NJ, I don't know anywhere else. Also, I don't believe there is a "one-size-fits-all" answer for your questions. Good luck, and feel free to drop me a message if you want to chat.