What kind of death did your 12 year old bike suffer? My bike is over 20 years old, I abuse it in many ways but it still suits my needs well enough. While several of my components ought to be replaced, I don't consider my bike anywhere near end of useful life. Might the best solution be repairing your old bike? If the frame itself is damaged it might not be - if one or two components need to be replaced it's probably worth fixing.
E-bikes are pricey, but they can be worth it as a gateway to increased cycling. A pedal assist e-bike is not going to make you lazy (you might get lazy with the type of e-bike that doesn't require you to pedal, but if you're concerned about an e-bike making you lazy you probably wont). Since your post didn't indicate that an e-bike would increase your utilization of cycling, I don't recommend getting one if frugality is your primary goal.
The most important thing about any bike is fit - simply is it comfortable for you to operate. You'll want adequate gearing for you commute. If you can, use gearing you actually used on your old bike to determine the gearing you need on your new bike. If the bike you are considering uses different sized wheels than your old bike you can use this formula to compare the distance a selected gearing drives the bike per rotation of the cranks: wheel circumference * front gear teeth / rear gear teeth. If you're considering a new bike, find reviews of the bike and/or it's components to get an idea of the quality. If you're considering a used bike, you'll need to evaluate the mechanical condition. The best values in used bikes are often bikes that need a little mechanical care - taking care of deferred maintenance (lubrication, replacing chain and gears, replacing brake pads, adjusting sifting, replacing control cables) can do a lot to increase the performance of a bike that has been neglected.