I came in under the old rules in 2008 and have been here for two years now as a student. I am completely opposed to using private loans, as they do tend to be more trouble than they're worth. I take out just the full Stafford amount every year ($20500) and it covers my tuition (£9800) plus gives a small amount extra (roughly £800 three times a year). When I first arrived, the exchange rate was in the middle of a huge drop from $1.75 to $1.35, so my first excess checque was meagre. A GRADPlus loan would easily cover the cost of living (at least here in Glasgow). I'm here with a wife who works full-time and that's enough for us to live modestly and travel.
To answer some of the questions, I think you can get your loans from whomever, but the ones disbursed through Sallie Mae (e.g. Regions) tend to arrive first. My first year, my loan was through a small bank that my in-laws use and the money always came two weeks later than from the bigger banks. Like Cali Girl, my university handles everything (even has a dedicated member of staff for it). They send me an email when the loan checks come in, I prod my supervisor to send in a basic progress report (he has it saved on his computer and prints it out when needed, just changing the date), sign the checks, and get the excess checque a week or two later.
Your university will have a good estimate of cost of living, but it is an estimate of 'poor grad student' living. That means getting food on the cheap and probably sharing a flat with someone else. In Glasgow, we have a monthly budget of £1000 (for all utilities, food, rent, etc) for living in a furnished two bedroom flat in an average working class neighbourhood (I'd rate the neighbourhood at a 6/10). If you were living alone here in Glasgow, I'd estimate a monthly budget of around £800 for a comparable situation (around £500 for sharing a flat). Following those numbers, you'd be looking at about £1100 for living alone or £700 for sharing).
For the Tier 4 application, I'm pretty certain you need £800/month for 9 months (or was it 12?) plus tuition in your bank and loan guarantees before you apply.