My wife had a 2007 320i e93 with about 75k on the clock, full BMW service history, and from experience, and subsequent confirmation of my disapproval from my friend/mechanic and ex chief BMW tech I would avoid the 2ltr petrol engine like the plague.
As mentioned above, you have to rag the shit out of it to feel like it's making any progress. Ran smoothly enough though, albeit gutless.....well...when it was running ok.
My wife's car would, at complete random and with no warning, stall, then get itself in a loop of the auto start stop starting, conking out , starting, conking out. During which time the dash would light up like a christmas tree, EML, the lot. Another of it's party tricks was running like it was on 2 cylinders, again with dashboard errors galore.
You'd have to stop the car, take out the key then restart and all would be well for an undefined length of time before it did it again.
I checked it with my diagnostic (the dealer level stuff), and couldn't find anything logged at all that would be related to such behaviour. Cleared all the other codes anyway.
It continued like this for a month or 2.
It went to BMW after this, as it was getting frustrating and they replaced the coil packs under a goodwill/technical upgrade.
Thought it was ok as it was fine for a few weeks, but no - kept playing up.
Took it back again, they checked it over and found no faults again.
Car continued playing up. I took a video of it on one of it's dropped a cylinder episodes, in the hope it might assist BMW. Dash lit up, engine making horrid noises. Popped the bonnet and videod the engine shaking like it was trying to escape from the engine bay. Turned the car off, waited, restarted and it purred like a kitten. No warning lights, nothing.
Didnt' even connect my diagnostic stuff this time, jsut incase it was inadvertently affecting anything. Took it to BMW again. No faults found at all...again.
Sold the thing, as it was just too much aggrovation and neither of us trusted it at all. Shame really, as it looked stunning on some nice rims and subtle drop.
Driving to part ex it was the most nerve wracking experience.
I'm sure there are a few good ones out there, but general concensus is that the 2ltr petrol of that era is a sack of shit and riddled with weird issues that seem to be undentifiable, so probably best to avoid if at all possible and the diesel (which is a better performer anyway).
I'd go with a relatively tidy e46 personally for £2k budget, and if it has to be a 2ltr, get the diesel (nothing really wrong with the e46 320, but it's a 6 cylinder 2.2 petrol - sounds nice but not that much go and quite thirsty to boot). The e46 318 is ok for a 4cyl, but not very quick. Personal choice for an e46 would be the 330 all day long, and wouldn't have thought insurance on an older car would be too much trouble, but appreciate it's a consideration.
Quick browse on autotrader and any e9x 320d will all be over 100k miles.....not sure if that's a problem, but you mentioned reliability, so some funds for maintenance will be required, even if it's just for suspension components, bushes, etc.
If spec isn't of concern (and to be honest, if you're buying a low spec e9x, you're not missing out on anything by getting an e46), then this looks tidy and cheap
https://www.autotrader.co.uk/car-det...to=2500&page=1