I think the best way to get the effective keywords with real low cost is to think like a customer. you may consider to add hyphen like 'seized-car repo-auction' or there is a habit to add '.' full stop after the end of word or phraze so you may consider keywords like "seized car." (all 3 types broad, exact phraze). Also there is a high probability of writing seize=sieze. Also a character can be wrong in 6 ways. like instead of typing 's' anyone can make 6 mistakes by typing a,w,e,d,x,z. You can consider adding brand names. like in 'full' any one can mistake to it as 'fuul' another way is to use seasonal keywords like near new year or christmas. You can also consider event driven keywords like world cup. synonyms and their spelling mistakes. famous word for a word like if your KW is 'pension' you must consider including '401K'
The best way to get the effective keywords with real low cost is not a way to get profit from AdWords. The only way, which gives profit is ti think about Return on Investement. You should pay cost, which is profitable for you. Low cost keywords do not mean proft.
Having a large budget may help you to get your campaign into profit more quickly, but I don't think it's necessary. And once you're in profit, it's irrelevant - a $10 per day budget would give you a better ROI than $100 per day (though less profit overall), as you can reduce your bids... But I agree that spending $5 per day is going to mean it'll take a long time to make changes to your campaign and see the impact.
If keywords are not relevant they will be of very high CPC. Only relevance can make the keyword cost low.
I think Google is just so clever. I have a blog on an Country where there is virtually no competition on adwords. i started my campaign and was able to pay 1cent a clicks but withing 2 days I day to increase it to 5cents a click and now Google wants 10p a click. there are only 2 or 3 at most other advertisers which are higly untargeted. My CTR is over 3% + and i think google will just not do it for 1cent
I am not sure of the logic that drives your bids up but as sites age I see costs go down. It may be less competition as others have bids raised or the topic becomes less popular (I have one older technology site that is getting 0.02 minimum bids now). If you can afford it, stay with it for a few months or years and you may see bids go down.
I've never seen any evidence that Adwords penalises or rewards older sites (though the latter may be true, though I doubt it plays a major part in the Quality Score). If you are seeing your minimum bids increase, your Quality Score is deteriorating. This often happens with new campaigns after a few days, as Adwords goes from having no history for your clickthrough rate to knowing that it's not very high (for your position). 3% is a good clickthrough rate for 10th position, but it's not very good for the top three spots. I very much doubt that Google's going to arbitrarily decide that they aren't making enough money, and increase your minimum bids manually.