Everything stated here is correct; if you want great sound you have to start with great location sound.
Great production sound means a recordist who can capture clean, hot audio and a boom operator who knows his/her mics and how to direct those mics noiselessly in cooperation with your DP.
Do not forget to record copious room tones, wild dialogs and wild sound FX; these are all a great asset in the audio post process.
There are five categories for audio post:
Dialog - Cleaning up location sound, ADR/looping, VO. ADR/looping is extremely problematic when you are working with young talent and even more experienced actors who have no experience with ADR/looping. It is much better to capture clean production sound; the emotional content of the scene is preserved.
Foley - Footsteps, punches, clothing, etc.; all the sounds pertaining to the characters. It is most especially needed when doing ADR to make the scene sound natural.
Sound Effects - Cars, doors, guns, etc.
Ambience - Traffic, birds, water, weather, etc.
Music - both non-diegetic and diegetic
The better the production sound is the more you can be artistic and expressive with the audio post process rather than trying to fix and hide poor location sound.
Blending all of these elements together to sound natural and exciting is the mixing or re-recording process. Here all of the elements can be used to enhance the emotional content of the scene.
As far as budget is concerned, most "Hollywood" productions budget about 10% for audio post.
Good luck finding a good production sound team.