I'm mainly replying to this because of your username: At The Drive-In are one of my favourite bands, haha.
I was in a similar position back in early 2006. I ended up choosing not to live with my current flatmates and moved in with friends, two of whom were a couple. We all got on really well before we moved in together but by the time we move out, only two of us (of 4) still speak. The couple thing was a issue for me after a while, not because they broke up but because I felt a bit left out when they just kept to themselves. In response to that I ended up being more solitary and avoided them and it just let to a meltdown. Not everyone's experience is like this though so don't be entirely put off. I'd just say make sure your housemates are easygoing and laid back and you're not likely to fall out about little things. Make sure you have good communication (because believe me, you don't know them at all until you're all living together) and it should be okay.
As for landlords: go with Unipol. They're the official university student housing association and landlords can sign up with them. To be a Unipol landlord you have to adhere to a code of standards that exist solely to protect students from the dodgy rip-off merchants (Park Lane, Your Student Home, etc etc, neither of whom are registered with Unipol). They also have a "Gold Landlord" thing which is for landlords who haven't had a complaint in 3 years. My landlord last year had this and he was really good - anytime we had a problem he was there the next day (or even the same day) and was always in contact making sure things were okay. I'm with Your Student Home this year (not by choice) and the best thing they've done for me is tell me I didn't give them my rent cheques in advance (I did) and then not answer my frantic calls and emails for a week, only to tell me "oh, we do have them actually, sorry" when I finally got through.
Anyway, Unipol is at
http://www.unipol.leeds.ac.uk and starts tomorrow (you can't search till then I believe). I'd strongly reccomend using it - the landlords will be backed up by an agreement designed to protect you and your money won't be getting nabbed: Unipol reccomends a deposit amount of £165 (well, that's how much it was in 2006) which is what my landlord last year charged. This year it was £250 and Park Lane charge £300+ - don't stand for that.
In terms of the actual househunting process: be wary of "salesmen"-esque people trying to get you to sign things or take copies of the contract etc. They'll try to worry you into signing up by saying the place will sell - don't listen, there's a surplus of housing in Leeds and they need you more than you need them. I remember looking round houses with no double glazing as the smarmy guy was like "You don't really need double glazing anyway, do you?" or houses with a bathroom cultivating a nice patch of mould where the guy just ignores it or says "Obviously houses will be professionally cleaned before you move in" - probably untrue. Be wary, they're all smiles now but afterwards things get dirty.
If places want you to pay a 'signing fee' when you do get contracts, again, be wary. Unipol doesn't do this so you're basically just giving them money for free that they don't even have to refund you with.
In terms of areas, these are the most popular locations:
Hyde Park: You probably already know this area, it's everywhere beyond the large park before uni. It's got a laid back 'alternative' vibe: there's a really good little rock club and various cosy pubs and bars, as well as lots of takeaways and shops. It's usually described as 'bohemian' and you'll usually see students with dreadlocks and baggy jeans wandering around. Houses are mostly Victorian terraces and crime is quite high.
Headingley: The yin to Hyde Park's yang. It's a bit more affluent and posh, with nicer houses and decor. Some upmarket bars and restaurants/shops but still lots of students. Higher rent though and it's further from uni, but a lower crime rate.
Woodhouse: Closest of the three to uni but puts off some students because of its reputation as a 'ghetto'. I live here now and while it's rumoured to be bad, I've never had any trouble. There have been muggings and attacks in recent years though, but then the same is true for Hyde Park. Houses are cheap and the closeness to uni is good, although I miss my Hyde Park friends sometimes.
There are other areas but these are the most popular ones.
If you wanna see what Leeds students rated the best landlords, there's a list here:
http://www.luuonline.com/house_hunting#a4 (it's from 2006 but still useful). I can only keep saying: don't be tempted by the ones "everyone's going with" that look all flash and have plasma screens in the office (Park Lane, I'm looking at you). How do you think they afford it all?! Places like that are notorious for deposit scams and since they have so many houses the service quality is diluted. Getting a place with a smaller landlord means a more personal service which is useful when your gas dies out in the middle of December.
Hope this was useful and if anyone else has questions, ask away.