the 80s and early 90s BMWs were actually extremely strong almost indestructible machines but since then they become endless money pits

I'm assuming that if you're considering a BMW, you know that they may not be as reliable as you'd think and required to be well-maintained. I currently own a 2016 BMW 428i @ 40,500 miles. I haven't had a single issue with it yet. You might say "the mileage is still too low and problems start at 100,000 miles". If you take care of the car like a baby (which is what I do and every month we have a little diagnostic date together), then no problem you'll get to 100,000 miles and perhaps more. I've seen people take good care of their BMW's and have lasted way more than 100,000 miles. But you have to be prepared for the worst. If something needs to be replaced, it's going to be pretty expensive to replace. OEM or OEM quality parts for BMW's are pretty expensive, but there are ways to get quality OEM parts for Euro cars for cheap like from FCP Euro. 

Now as for your question...I'd say the 2006 E90 325i OR the 2008 E90 328i were one of the most reliable BMWs within your specifications. If you want reliability with BMWs, try to stay away from the turbocharged engines, but that is going to cost you power if that's what you're looking for. The 325i has a 2.5L straight-six engine producing 215 HP, and the 328i has a 2.8L straight-six (same engine but the 328's is slightly bigger) producing 230 HP. It's not too bad, but it is a decent amount of horsepower compared to the average sedan. Hope this gives you an idea on which BMW is right for you. I think most people here HATE BMWs because Scotty bashes on them in every video...but if you do your research not all BMWs are bad.

I had a 2008 BMW 335xi coupe and LOVED it. However, I bought it used and by 40k miles the following things needed replacement:

1. A/C Compressor

2. Driver's side seat rail

3. Hood peeled and needed repaint

4. Various bulbs 

I definitely enjoyed the car, but just those few items cost a small fortune. Fortunately I had a great warranty I purchased and only had to pay deductibles each visit.

If you are looking for $5000 or less, the E90's mentioned above would be the best option. Just know you will have repairs and they won't be cheap.

Break My Wallet

Late 90s E46s were also decent vehicles, some think that gen. of 3 & 5 series were the "golden age" before tech and complexity started going beyond a reasonable tradeoff.

RWD Lexus (IS & GS) and Infinitis are also worth looking at if you aren't necessarily into getting a roundel.

BMW if you must, … in a nutshell:

Compact: stick to E21, … stay away from E46

Intermediate: stick to E34, … stay away from E60

Large: stick to E38, … stay away from E65

… skip all others, … not worth your time! (Unless you run to an exceptional one, … near new condition and very cheap.)

Watch out for rust, previous owners modifications. Nothing matters more than sound body and completeness of the car - all stock. Be prepared to spend lots of idle time awaiting ordered parts shipments.

Best,

F.S.

BMW - Big Money Waster. My boyfriend  had one for 5 years and we will never get one again.