But there are other alternatives as well that if one is creative can make it work within those constraints.

They have access to the data you need to make wise choices and they have the experience to guide you through the analysis, acquisition process, and operations.Hope this is helpful! 

We ideally would like to live in this property for 1.5-3 years cash out at about 10K - 15k and then make the jump to a more expensive multifamily home, duplex, or triplex which we can rent out.Any thoughts on this strategy or suggestions on alternative strategies?

I've lived in Memphis for 20 years (by choice!) 

Stain is ~$40/bottle and sealer is $200/5 gal.Tile counter tops are really cheap to install.If you do exterior repair on soffit or fascia, always go back with hardie, less maintenance over time.Places like surplus warehouse will give you a 3% landlord discount on doors and windows (and they're already dirt cheap).Capex is important to keep track of but with so many alternative options to pay for the expense, I don't stress too much over it either.  

Lastly if we would be forced to lose the equity by taking the loan on the ARV, what's a good alternative option for financing the rehab separately from purchasing the house?

The alternate option I came up with was to remain in my primary residence and rent out the spare rooms to get more cash flow coming my way.

However, with family and kids (one toddler and one infant), it's unlikely to be of viable choice to us.

Some have 30-60 days to recover, some longer.You need to check either the laws of the state you are buying, or perhaps as an alternative you can check with either the appraisal district, the tax district, or the attorney representing the tax authority where you plan to live.  

More than half say that the few quality assets available are overvalued.I present the conclusions of the study, Trends in the Real Estate Market in Europe 2017, prepared by PwC and the Urban Land Institute:TRENDS OF THE REAL ESTATE MARKET IN 2017The expectations of investors in the European real estate market in 2017 are marked by the lower availability of quality assets, lower economic growth and lower profitability:It remains a very attractive market thanks to the relationship between risk and profitability, but most respondents believe that last year's profit levels will not be reached.Investors believe that the impact of Brexit will be limited to the British real estate market and will not significantly affect investments in the rest of the EU:To the question of which alternative sectors can be attractive for investors, the most frequent answers are: Accommodation for students,hotels,nursing homes,shared service offices.Germany, the United Kingdom and Spain are the three most attractive European countries to invest.