I thought I'd offer some advice to new and experienced players based on what I've learned while playing House MD thus far. I'm only level 14 so my advice may be incorrect and/or inefficient. Please feel free to add your own advice for others!
Tips for gaining Favor Points
Try to have at least one friend specializing in each of the six specialties. This will allow you to complete an assortment of ward cases, unlocking more diseases in the disease database. If you cannot get or don't have friends for each of the six specialties, it isn't going to hurt your ability to collect Favor Points.
Send clinic patients to the ward based on the specialties of your friends. This will allow you cure the patient immediately instead of having to wait 6 hours.
Don't forget your staff doctors (Chase, Foreman, Taub, etc.). They can cure any ward patient immediately. I will usually send clinic patients that don't match any of my friends' specialties and use the staff doctors on them to try and unlock those diseases in the disease database.
Try to do this first thing each day/every 24 hours. This will allow you to focus on collecting supplies and cash the rest of the day.
I currently have 11 friends and 2 staff doctors unlocked. This nets me 13 Favor Points each day.
Tips on collecting supplies
It does not cost energy to queue up pill scripts in the pharmacy, only to collect the pills. I try to queue up one of each pill script, selecting the ones that give the most pills. It takes more time, but costs less cash per pill.
Send a variety of clinic patients to the pharmacy. I will try to send an assortment of patients to the pharmacy to evenly collect the different supplies. That way I am not short on any one supply should I need it to complete a ward patient or part of the critical case.
Tips for collecting cash
Only tip I can think of is to send clinic patients to the MRI and Blood Testing rooms when you need a large income of cash. I haven't had the need to send patients there too often, but this may change as I get into the higher levels. Also, upgrade your equipment when your cash income allows. I don't know how much of a difference it makes, but again I am not that high a level yet.
Tips for the Critical Cases
Don't rush through the Critical Cases. They take up the most resources, especially Favor Points. I find that when I rush through them I quickly run out of resources. Take your time with them and you'll find the game a little less frustrating.
Again if anyone has any other tips or advice please feel free to post them! Hope these are of some help to both new and experienced players alike.