Where do i start here, you can not put your car up as collateral on your house, not how it works. It has been stated here what it takes to buy a house, 3 years of proof of income through taxes. In 2005 you could have got a loan with nothing, but that is why the housing market crashed, doesn't work like that now. A partner is never a good idea, if you can find a way around it do, it never works out the way it is supposed to.
Now on to where are you going to sell it from? The same place you are growing? The issues in that present themselves. If you get busted for selling they find the grow. I never said that SELLING 2 ozs a week was an issue, i said PRODUCING 2 ozs a week is the issue, takes a lot of money in equipment, a lot of learning for timing and all the things that can, and will, go wrong. Think of it this way, to start producing 2ozs a week, expect to put at least $2000 more like $4000 just into equipment, then you have to set it all up yourself, so you need to know plumbing and electrical not to mention some basic construction. Now you have to pay the rent or mortgage for at least 3 months before you have ANYTHING to sell. Not to mention that electric bill and come up with nutrients and etc as it is needed.
You have moved a long way from talking about an apartment and a $500 a month job. So if you really want to do this here is what i would do....
Find a rental or rent to own house, make sure the lease is in your favor as much as possible, and plan to maintain everything in the whole place yourself. May need to buy a cheap phone to put down as your "employer" for the landlord to call and you (or someone else) to answer "Bills shoe shack" or whatever and say you are employed for X dollars a month and you a great employee. Most landlords of houses will treat you as you present yourself so be professional and you will be portrayed as professional. If your $40,000 car is a kids car (nothing personal) use somebody's car thats a little more mature. Sell yourself right and they will never bother you, as long as you have them the rent check on time. Checks would be better to pay the rent with, even if it is a little red flag to the bank, less so to the landlord.
Now it gets tough, try to spend as much as you can but have enough to live for 4-6 months with no return on investment. That will give you some room for error. Now use everything you learned growing at moms house and put it into true action and see if you can get full production. Good luck, stay out of apartments its easier to get into a house if you try hard enough, and watch the details any time you lie about anything. A lot of people work for very small companies, so you don't need to tell them you work at the local Ford dealership, cause their brother could work there. Sorry if i was negative at the beginning, you sounded like a kid who had no clue, and was looking to end up in jail.
I will leave you with this, Loose lips sink ships. So don't tell anybody anything and you could do a lb a month out of a bedroom.