Vanguard requires a $3000 minimum investment and minimum 1 share for their ETFs; see their ETF Fees and Minimums for more details.
As such, with $1000 initial investment and $100 a month, this would be a poor choice; while some brokers might allow you to buy fractional shares, with ETFs I don't think this is common unless you're paying a decent bit of overhead (which negates the point of the ETF).
Note that Betterment is going to charge you 0.35% plus the ETF fees (which average 0.14% or so), so you're going to be charged around 0.50% in total. That's probably not the worst thing in the world for such a low balance, but be aware of it. Once you can get over the $3000 level, I'd suggest transitioning to Vanguard or someone else who won't charge you the extra 0.35%.