Some decent neighborhoods in Southwark (London)?

Hi,
So, tomorrow is my flight to London.  I have been looking online for months now to find a home near Southwark (I will work near the Peckham Rye station).
I have read all sorts of reviews on upmystreet and have saved hundreds of properties on the usual rental websites.
My concern is that nearly every neighborhood in the general Southwark area has had negative reviews from folks. This is making me a little nervous.
I currently live in the Gary, IN area-a place with super high crime and poverty. I say this because perhaps my tolerance for seedy neighborhoods is higher than others. I am wondering if perhaps these reviews may be a little embellished? See, my measuring stick to say a neighborhood is dangerous is pretty high based on where I grew up.
But, since I am not going to be there until Tuesday, I cannot say for sure. In the meantime, I am setting up appointments with letting agents but I just don't know how to trust.
Anyone out there can give me some advice on a good neighborhood? I will need an area with a decent catchment area (I have visited the Ofsted reports) but we will most likely keep our daughter in a Montessori method school for the time being.
I am a social worker, so I am not going to making tons of money  Our budget is roughly 1200 GBP per month for rent, exculsive of utilities, tax, etc.
I am not opposed to having a public transit commute to up to an hour but anything beyond that would be crazy. I have also looked into Kent but still the reviews are all over the place.
Can anybody out there give me some slid advice on this? Thanks so much!

BTW, excited that I am finally moving! 

On the whole, Southwark is safe if you're not stupid about things. Most people who run into trouble are looking for it. I've been here a year and haven't seen anything worse than some creepy drunks.

There are some absolutely lovely areas of Southwark, and then there are some absolute holes. Basically, the closer you get to the river, the better (and more expensive) the area is. I live on the Old Kent Road near Burgess Park, about a mile north of Peckham Rye. I don't really like it here, but it's not the worst area and I don't feel threatened walking around. If you're used to rough areas, you might not mind these bits of Southwark too much. I wouldn't recommend anyone with a small child to live near Peckham, but that's possibly just me - I was raised in an incredibly safe suburban neighbourhood.

You might look into living near a train station on the same line as Peckham Rye or somewhere with a direct bus to Peckham. I can't say I'm an expert on any of the areas, but I've found parts of Herne Hill, Clapham, Streatham and Dulwich to be nice. Within Southwark I prefer areas around Borough, London Bridge and Tower Bridge/Shad Thames. Some of my friends live in Camberwell and enjoy it; I'm personally not a fan, but that could just be me!

If you're set on Southwark and want a decent estate agent in the area, London Village Apartments have been really good for us the past year. They're quite a small team and if you end up dealing with Ben, he's an incredibly friendly guy. http://www.londonvillageonline.co.uk/

I can't say I know anything about good areas for families, but if you have any other questions about Southwark, feel free to send me a message!

Perfect! Thanks so much! This is exactly what I need, all the reviews on upmystreet vary and I can't really gather anyhting useful. I will definately look into these areas. I hope to get a viewing arranged for Tuesday evening. My husband and daughter are arriving just 4 days later!