Everyone must invest based on their personal circumstances. Those circumstances include available time, available money, knowledge, and (very importantly) risk tolerance. The last two seem to be in short supply in your case. AND there is NOTHING wrong with that. We all start somewhere.
To add to the points made by others above, I'd support the previous suggestion that you find someone who knows the business and can help you run the numbers; has experience in evaluating properties; has crews in place nearby; etc. YOU do all the leg work of the remodel AFTER they "bless" the property.
Experienced people can tell a LOT from the outside and just looking in windows. They also know how much cushion to build in. A two minute review (NOTHING to rely on) says that the home is worth around 100K, maybe more for a top notch rehab. If you can get the home for 40K or less, things could work out well.
And HERE is the GREAT part: If the mentor says it is a great deal, money is not an issue. The Mentor may pony up; HML will line up (especially if you have a known mentor that they've previously done business with); it is easier to approach family and friends; you can just wholesale it to the Mentor for some easy cash and NONE out of your pocket; and there are probably more ideas that more experienced people here on BP can add. But the KEY point is money is much less of an issue if the deal is vetted by an experienced person and deemed good.
Stating is another way and from a different angle, having an experienced person in the greater Milwaukee area in on the deal provides a LOT of "peace of mind". They are NOT going to go in on a deal that does not make sense. Just meeting them at the property to review it and discuss the numbers (do a LOT of prep work on values BEFORE you meet with them....it is on a divided hwy, that knocks down price, etc) will teach you a LOT.
AND, if (<--- see "IF") they say it is a good deal, your risk of doing the fix and flip just dropped like a led balloon. You could do ALL the work (interfacing with the contractors, etc.......but, keeping the mentor informed of every step....having the mentor do onsite inspections at critical steps...) and offer them fifty, sixty, or seventy percent of profit as "tuition". That cuts your return in terms of dollars, but you can't price the value of the knowledge (and peace of mind that an experienced person is watching your back) you'll have as you "get your feet wet".
Also, experienced people will JUMP on a deal and WILL make it happen, if (<--- see "IF" again?) it is a great deal. So, the short timeline is not an issue IF it is a great deal.
I envy you living in an area where you can purchase a house, CASH, for what is barely a twenty percent down payment here. Your risk is largely mitigated by that fact alone. Your gross family income can purchase a decent/nice house in full. Our gross family income is a fifteen or twenty percent down on a fixer.
No "woe is me", just perspective for you.
In fact, I want to stress that you are right and correct to be cautious. You can lose a LOT of money very, very quickly in REI. But, there are many, MANY ways to mitigate risk. The low housing costs in your area are a HUGE benefit to you and your family. Your family income and family frugality is another HUGE advantage, especially when combined with the previous point about housing costs in SE WI. Finding an experienced flipper in the area and showing them the deal and your available resources will substantially cut any remaining risk. There WILL still be risk. But substantially less than you "winging it" on your own.
Finally, if the mentor/partner idea is a non-starter, I'd suggest that you "get your feet wet" by loaning a portion of your risk capital to a flipper. You may earn as much as 12% plus points. (I don't know the market in your area) And if done properly, your investment is secured by the real property, AND you are also building a relationship with someone who can do the mentoring outlined above in the future. Double win. Vet them as you'd vet any entity to whom you would lend money. Visit previous projects, ask for references, etc, etc, etc.
As far as the Ramsey method. I must confess that I've not studied him. But, having a loan on your primary residence (assuming that you have at least twenty percent equity in the property) is NOT a bad thing. Instead of paying it down, I'd be investing at a rate higher than the mortgage rate. Funding a HML at 8% or more should beat any return that you'd get by paying down a 4% (or less) mortgage. AND, the HML investment is secured by Real Estate.
Sorry for rambling.
I hope this is received in the constructive manner it was intended.
Good luck. God Bless. And Go Get 'em!!!! i.e. Just Start!!! You are in a far superior position to many newbies here on BP. Be cautious, mitigate risk in any and every reasonable way, but START. You'll be glad you did.