If you move a 401k to an IRA it is automatically classified as a Rollover IRA - it acts as a traditional IRA but shows that it was originally some form of company sponsored account previously. I think turning this into a Roth (which would be extra steps involved) would be a very wrong move. You would pay taxes on the entire amount as if you earned it along with your current salary for this calendar year, and pay out lots more in taxes. So don't turn this into a Roth!
Definitely go for a rollover IRA, and then invest in whatever you'd like. You don't even need to move it over to Vanguard if you don't want to; Fidelity is actually a pretty good company as long as you stay away from their managed funds, which is likely what you were restricted to with the 401k. Once you turn it into an IRA you can invest in any Fido fund including their stellar Spartan series, which is what I have. Spartan offers many equivalent index funds similar to Vanguard. In some cases, they offer slightly better expense ratios.
And no, you don't pay any taxes on 401k/IRAs until you withdraw the money from them; selling off funds to purchase different ones inside a401k/IRA or performing a rollover general aren't taxable events to my understanding (and I've done both). Paying taxes later when actually drawing on the account is possible, but that is also contingent on your taxable income bracket (if you are in the 15% bracket or below - you may pay no taxes on dividends/cap gains).
https://www.bogleheads.org/wiki/FidelityThere
are a few reasons not to turn it into a rollover IRA - if you're in a state like California, 401ks have better protection against judgements and bankruptcy than an IRA, or say if you are getting institutional shares only available by being in the company's 401k program (unlikely in this situation, and anyway the Spartan series probably offers better choices).
I weighed the benefits of rolling over, and decided it was in my best interests to, so really you just need to confirm the same for your situation, and do a bit of reading like the bogleheads link above to see if all of that makes sense for you. Do confirm the info I've given here with a rep to make sure (the pros/cons of rolling to an IRA). ;)