Okay, let's see if I can help.
Firstly, no, you don't have to wait for your visa before booking the flights, but it's usually advised that you do, just in case you pay for the flights and then get refused a visa - you'll have wasted all that money.
It's not often that you will get refused a student visa, but nothing is 100% guaranteed until you've received it - so it's really up to you to decide whether it's worth the risk to book before you get it.
You don't have to buy return tickets to get through immigration - your visa should have your dates of study on it and as long as you can tell them that you intend to return home at the end, it should be okay.
In terms of which flights to go with, it might be easier for you to pay more and go with the group flight as everything is arranged for you. However, it is possible to do it yourself if you want.
A quick online search has shown that you can fly from Phoenix to London Heathrow for about $800-$850 (round trip) on Yahoo travel (the cheapest one-way I can find at the moment on STA is $530 from Newark to London). Most flights are overnight and will get you into London between 7am and 9am. It is only a short train and tube journey into Central London from there (you can get a tube pretty much right to UCL, as it is so central), but the only problem might be the length of the immigration line (I've spent 2.5 hours going through immigration in the US before), so it's not guaranteed that you'd get to the office by 12pm.
If you decide to go with independent travel, you might need to arrive a day earlier and stay in a B&B for a night before going to the orientation office.