I personally use Fidelity (the decision was driven by the fact that my employer uses Fido as administrator for our 401k, HSA, and other benefits so I already had Fidelity accounts when I started seriously focusing on investments).
I think the basic index funds you need to build a simple portfolio are comparable between Fido and Vanguard, with Vanguard having better bond fund offerings. One difference (from what I read) is that a brokerage account at Fido can hold both mutual funds and ETFs/individual stocks, so you only need one taxable account. At Vanguard, I think they make you open 2 accounts (one for mutual funds, and the other one a true brokerage account for ETFs and stocks), but I don't think that is of any consequence.
You have to do some reading and educating yourself in order to decide on your AA (you need to figure out your risk tolerance). I think both Vanguard and Fidelity have some questionnaires on their websites that walk you through a bunch of questions and scenarios and help you with that. Spend some time thinking about it. Also, there would be nothing wrong with starting, say, at 80/20 and slowly working to the ultimate AA you want.
Specific funds to build a portfolio - read this
http://www.bogleheads.org/wiki/Lazy_portfolios:
At Fidelity, look up anything designated Spartan. I use FSTVX (Total US Market), FSGDX (International), FSITX (US Bond Fund - in tax advantaged accounts) and FTABX (Muni bond fund in taxable - totally optional, most people don't have bonds in their taxable accounts)
At Vanguard, Bogleheads recommend VTSAX (Total Market), VTIAX (International) and VBTLX (Total Bond Fund).
The general rule is to keep your entire bond allocation in your 401k and/or IRA, and invest taxable in stocks (US and international).
As to moving your taxable investments, it looks like you would have about $2.5K of taxable gain after all the transactions, so you need to decide if you want to pay the tax on it or not. You can move investments in kind without triggering a taxable event but that is more complicated.
ETA: I also felt overwhelmed when I first started focusing on my investments 2 years ago but have done lots of reading and research and asked lots of questions to arrive at a certain level of comfort. I am not a sophisticated investor but I now have a good handle on the basics that is sufficient to serve my purposes given my style of investing (buy and hold, long term, low cost index investing focused on simplicity and tax efficiency)