Welcome to FlyerTalk. You've come to the right place. I also recommend frugaltravelguy.com and his e-book for a more narrative explanation.

2% cash back cards currently available:
Capital One Venture Rewards Visa: 2% cash back redeemable for travel, $59/year, but first year is free
Fidelity AmEx: 2 WorldPoints/$
Fidelity Visa: 1.5 WorldPoints/$ for the first $15k/year; thereafter, 2 WorldPoints/$

WorldPoints are redeemable for $1 or 1 mile on Aeroplan (a good Star Alliance program), making the Fidelity cards the only cards that can earn 2 star alliance miles/$.

Hotels can cost more than airfare, so you may want to study their loyalty programs and credit cards too.

Especially consider Starwood AmEx and the various AmEx cards that earn American Express Rewards points, as both of these offer redemption above 1:1 for airline miles, and specials for converting these points to various programs roll around periodically, and these cards also tend to offer bonuses for high annual spending levels, such as the AmEx Open for Business offering a 50k points on the first 10k spend, and then, annually, an extra 25k points for $50k spend, which would effectively be 1.5 points/$, which can work out to more than 2 miles/$ using some mileage transfer specials.

For people like me with lower spends than you, the biggest benefits are in playing the sign up bonuses, so I will mention the topic just so you can be aware of it. You can get $500+/month by applying for the record high credit card signup bonuses that are being offered these days (for reasons I don't fully understand). If you want to average no more than 1 card per month, you can probably limit yourself to airline card offers of 50k miles for Star Alliance carriers and over 50k for all other cards unless there is something special about that program that would make it worth not waiting for their best offer. In the past 6 months we have seen the following offers:

75k/100k Citi American Airlines AmEx, Visa, business Visa (I got all 3)
up to 100k Capital One Rewards personal and business (was possible to get both)
50k United (most recently limited to their elites)
50k Continental
100k British Airways (new last week)
50k Lufthansa (new this week)
75k AmEx Rewards (new this week, targeted)

Regarding using credit cards to pay vendors that don't accept them directly, the possibilities that I can think of probably aren't worth your time, but I will mention the ones that come mind so you can decide for yourself.

If it's still worth the miles if you have to pay a ~2.5% surcharge, chargesmart.com (certain utilities and loans), williampaid.com (rent, don't see any prohibition on using it for commercial office space) and the various services for paying tax by credit cards. For the services that accept AmEx, you can buy gift cards from AmEx at a 1.6% discount, via bigcrumbs, subject to various published and unpublished limits. Do not use Citi cards to purchase AmEx gift cards, as Citi reclassifies them as cash advances. Other credit cards are generally OK and earn their usual purchasing rewards.

One possibility that I don't think I've seen mentioned before is getting your vendors to accept gift cards in payment, perhaps in exchange for a 1% bonus. AmEx has higher limits for purchasing "business" gift cards.

Looking toward the near future, you may want to keep on eye on the brewing alternative payment system turf war (PayPal, Amazon Payments, Serve, ZipWire, and Visa's new initiative with CashEdge and FiServ) as I would expect some loss leading promotions.

You can also buy dollar coins from the US mint for $1k/10 days, which you may be able to use to buy money orders from a particularly tolerant cashier. Also, in practice, some debit cards that earn rewards on PIN transactions that are not supposed to reward purchasing of money orders do in practice earn miles when the money order is bought from some stores (presumably because the bank can't tell what you spent the money on).

If you have some float with the money you are going to send to vendors, there may be a couple of additional opportunities. You might consider piping it through a brokerage account to qualify for their sign-up bonuses, or storing the float in BankDirect (but I worry about possible tax issues if the miles are "interest" rather than "rebates"). Also, I believe that Citi and BankDirect both have some small promotions where you get some miles for setting up bill pay, but I don't think the rewards get bigger for paying a substantial volume.

Anyhow, there are dedicated threads in the MilesBuzz section of FlyerTalk for almost every offer that I have mentioned above. I know I haven't done any of these topics justice, but I hope this overview will give you some ideas for further research. Happy reading.