Chemistry vs Biology
-Chemistry is much less competitive to get into (many providers still have places for a September start!)
-Chemistry has slightly better career prospects as it is in higher demand by schools
-Chemistry gives you a much greater training bursary (around 10k more with the same degree classification!)
Then again, as a Chemistry teacher i'm hardly unbiased.
Universities
-Personally, though i went to Cambridge as most of the work is done by the schools the university doesn't really factor into it that much. Getting a more "prestigious" university might help very marginally getting your first job, but that's less of an issue with shortage subjects anyway and if you're a good teacher they'll take you from anywhere. My advice, if it matters to you, put a more prestigious uni first on your list.... tbh if you apply for Chemistry you've got a good shot of getting in
Experience
Get as much as you can in a range of schools. September, around Christmas, any time that universities are on holiday and schools aren't. You want a week or so's experience ideally before applying, but if you're really tight then organising something for easter and putting it on your application as something that you are going to do will also help.
Living in/commuting
-Firstly, with placements you are going to have to commute full stop. I lived in uni and had over an hour each way to get to my placements, just part of life if you get the short straw. The advantage of living at uni is that you then don't have to commute for the lectures.
-Secondly, living with other PGCEs is amazingly helpful. Some of my best current friends i met on my course, and the support of everyone having the same issues to deal with and the same assignments and deadlines is amazing. No one knows what it's like to be a teacher except another teacher.
-Cost wise, if you're netting 15-20k bursary, living out isn't going to be an issue. In fact you'll be earning considerably more per month than you do as a full teacher, the 20k works out at 2.2k per month, which is more than i earn 4 years in.
Job
-I wouldn't worry about it. Start looking in Jan/Feb, and be prepared to have to sift through a lot of advertisements to find a job you want. If you are more flexible location wise it's a big help, but there are a lot of jobs out there. I think pretty much all the decent chemistry teachers on my course had jobs sorted before easter.