Slingshots are nice if you're happy to carry all your gear on one shoulder and not be able to swap it. Personally I found it ok to begin with but, especially on longer days like when I'm holiday, it's quite tiresome.
I'm also in the market for a new bag and at the moment I'm trying to find a Kata 3N1 to try out. They are rucksacks with removable, adjustable straps that can be set up to act like a sling, a crossover rucksack (so you can turn it into a sling immediately by unclipping one strap), or just a regular 2-strap backpack for the long walks.
The 3N1-10 is around £50 I think and appears to be enough for the camera + attached lens (not too long), plus 2 extra lenses and maybe another one in the top compartment.
The 3N1-20 is £65+ and is the larger brother so can take 3/4 extra lenses I think.
You can get tripod holder attachments for £12 too so you can attach one to the back of the bag.
My only concern is that I have seen people complaining about the straps being too thin so they aren't as comfy as they could be. They look pretty chunky to me from the photos so I'm keen to try it myself. I was also thinking that I could quite easily slip some thicker strap covers over the top if needs be. I've also seen complaints about the zips not closing fully so potentially letting rain in. Again, I want to see one in the flesh.
My other option is a Lowepro Fastpack 200.
It's just like the Slingshot in that it's side loading, except it's a dedicated backpack, so it won't dangle from your neck while you fiddle with your camera; you'll have to make sure you hold it steady with your elbow while you grab your camera out, etc. I'm not too keen on this, so I'm eager to try and 3N1 as soon as possible.
Are you interested in the sling functionality at all? Being able to access your gear while standing?
Keep us updated on your findings because it sounds like I'm after a similar thing to you too.