Hi Christopher!
I haven't actually done any deals yet but am in similar shoes to you so I thought I could chime in. As you mentioned, it all comes back to your tolerance for risk. Could you buy a property with a $4K down payment ASAP? Absolutely, but you could be stuck with a big expense if something goes wrong early on.
Regardless, you are taking the right steps by saving aggressively to mitigate your risk. There are 2 things I might suggest to mitigate risk if you are uncomfortable proceeding with your current savings: (1) The better a deal you find, the less risk is inherent to any purchase you make. If you purchase a $200k property at $120k, you have more flexibility if anything goes wrong because you already have $80k in equity (this can also be achieved through renovating and forced appreciation). This brings me to (2) - look into a potential 203(k) loan to fund not only your purchase but your renovation. This way you can make your money stretch further and potentially gain some equity early on, which can be borrowed against for another deal or refinanced to reduce your debt servicing cost.
Like I said, I still haven't done a deal so I am just saving like you and investing my time as much as I can to reading here and studying up to be ready to make a deal when the opportunity presents itself. Regardless, I would keep saving the $1k a month as it can't hurt to be saving extra $$$. Hope this was at least a little helpful, best of luck!
