This is a common question, and the search function might bring up some more threads on the subject.
In brief:
If you think you WILL need that money in <3 years I would certainly suggest you put it into a secure savings account
If you think you WILL need that money in 3-5 years it's a personal call
If you think you won't need that money for >5 years it should be in the market.
given that you say you "may bounce around for ~10 years [before buying a home]" I'd strongly recommend investing everything in the market right now.
You'll notice that I put "WILL" all in capitol letters. That's because how certain you are that you will need this money for a downpayment has a lot to do with where you put it. If you have flexibility and aren't dead-set on buying a home in x years, then you can choose to put the money in the market and let that help dictate whether or not to buy a house in several years. If you go this route and the market drops, you can decide to keep renting for a few more years until you can save more for the down payment.
Regardless, with $2,000/mo surplus you could at any time start piling money into a savings account and rapidly have a large downpayment. You should do this whenever purchasing a home goes from "sometime years down the road" to "possibly in the next 1-3 years". If you later decide against it - no worries, just take all that accumulated cash and invest it into the market.