I would like to avoid rolling the 403b into a Vanguard Roth. Would rather just slap it into stocks and let it ride for 10-15 years.
I think you may be confused about what a Roth IRA actually is. It seems as though you might think that Roth and stocks are mutually exclusive. They are not. A Roth IRA is just an account where you can put investments and have certain tax benefits. You can own stocks in there, or mutual funds, or bonds, or even leave it in cash if you want.
You have a few decisions to make.
1) What company do you want to hold your investments with? Vanguard? Fidelity? Schwab? Wealthfront? Someplace else?
2) What type of account do you want to use? To have no immediate tax consequences you'll want to roll your traditional 403(b) money into a traditional IRA and Roth 403(b) funds into a Roth IRA. If you move your traditional 403(b) funds into a Roth IRA, you'll owe taxes on the converted sum this year. Probably not what you want.
3) What investments do you want to own? You seem to have settled on VTSAX. Given that, Vanguard is probably the best option for (1) because they won't charge you any transaction fees for buying and selling shares of VTSAX.