I know someone else mentioned house hacking, but it sounds like your family is not going to be down with that strategy... My family is the same way, so I get it.
The next suggestion I go for is a live-in flip. Use your VA loan to get a primary residence that needs some love, find something that requires primarily cosmetic work, get your hands dirty, and make it a gem. The beauty of this is you have a couple of great exit strategies when you're done.
1. Live in it for two years and sell at the end of the two years, freeing up more of your VA eligibility to buy the next one. You also avoid the capital gains tax by living in it for two years. Now you have cash to put down on a rental property conventional loan, and you can go and grab the next live-in flip with the VA loan.
2. after six months to a year, move to the next property, where you can use the remaining balance on your VA eligibility to acquire and rent out the first property. Then rinse and repeat the process until you are out of VA eligibility and refi the first property into a conventional mortgage.
The key here is that you need to add that sweat equity to the properties, providing a cushion for market fluctuations and increasing the rental potential for each home. I will echo the others. You should just get started; don't get into analysis paralysis trying to find the perfect strategy.
The only downside here is that you will be doing a lot of moving, so make sure the family is on board, or else after the second move, you may be spending all your profits on a marriage counselor... just kidding.
