If you've had a knee injury you'll need the days off inbetween. Also, the body improves fitness better when you give it time to recover, it's called super compensation theory or something like that! That and if you go everyday it becomes bit of a chore and not so enjoyable. I would say starting off stick to a day off inbetween runs at least, maybe once you've done it a bit more you can add in extra runs- the best way is just to listen to how your body feels really. You'll soon know if it's too much.
In terms of 'toning' up, you also have to consider your diet. If you're eating habits aren't good then exercise won't help- even snacking is probably adding more calories and fat than you realise. If you keep a food log then you notice just how much you're actually eating! (This is what I did, it's very surpising!)
If you're eating is fine, then yes weights are the way forward. I personally go to the gym and only pay £10 a month, but if you can't afford that then you could invest in some dumbells as a one off payment? Or use household things! Heavy tins and jars might help. And things like squats, press ups etc are all going to help build up your strength, so don't discount them. I still come home and do squats, lunges, press ups and sit ups after shorter runs. At the gym I tend to cross train as alternative cardio and then use the resistance machines and free weights.
I've taken up running a lot more seriously, so bought some decent trainers (£70) and got my gait analysed. If you go to a proper running shop you can normally have this done for free and you're not obliged to buy anything. You can then go to somewhere cheaper like sports direct and tell them what kind of support you need and pick up an OK pair for about £30 or so.
And finally, in terms of the change in fitness? I started off like you, I'm now running a 6 miler in 2 weeks time, and a half marathon in a few months. So stick with it, it's worth it!
Also make sure to keep an eye on your knee! Soon as I started upping my mileage my knee didn't like it.
Good luck!