You should certainly not use your main personal cards on the behalf of the business, simply for segregation of accounts to assist bookkeeping. (This goes for all founders from day one. Credit cards are available like candy; get one for business use and business use only early, early early.)

Whether you get a "business card" is less important; for many founders/companies they're substantially harder to get than personal cards. You'd think this distinction would matter a lot, but practically speaking the principals of most small companies will be asked for a personal guarantee on any card issued to the business anyhow, so that's a distinction mostly without a difference. Typically they also come with worse protections and terms than consumer cards. (e.g. I have two cards from BoA, one in the name of the business with a personal guarantee and one issued to myself as a natural person. The business card has 1000 basis points higher APR, worse protections, lower limit, and an equivalent rewards program.)

As to which card you pick: there exist copious websites which will attempt to sway your opinion on this, mostly to earn an affiliate commission. There also exist a lot of people with strange hobbies online, and maximizing the value of CCs/reward points/etc is a hobby which is quite well-represented. I'll save you a few hours: the SPG (Starwood Preferred Guest) Amex almost always wins. Personal favorite perks: bonus points awarded for Uber trips during hotel stays (i.e. business travel, when I consume a lot of Uber), free Wifi at SPG properties and Boingo (sadly not Gogo), and a very favorable SPG-points-to-dollars-saved-on-hotels ratio. (I recently took a free night in Austin for 16k points; due to it being a high-demand weekend the hotel was quoting about $500 for a cash stay. This implies a 3.1 cents a point valuation, which is much, much higher than points are typically worth -- Delta miles and IHG points, for example, are a lot closer to a penny apiece.)

Obligatory maximization advice:

1) The most important thing you can do with business credit card statements is make sure you do not forget to get them entered into your books. Your tax rate on the marginal dollar of profit is likely to be 30%+ -- this totally swamps the value of your points/saved interest if you screw up even a page worth of CC statements once a year. (Ask me about the time I almost had $14k of marginal income imputed due to a page which fell on the floor at tax time, for a $5k extra tax bill.)

2) Selling more software is a much, much faster way to make money than exploiting the difference between a 1% cash back (trivial) and the Optimal Possible Business Travel Planning. The people who invest a lot of themselves into travel hacking largely do it because it's a fun, somewhat intellectually engaging hobby.

Websites to read on this topic (and, like mentioned, they make their money when they get you to apply for a credit card):

ThePointsGuy.com
Ramit Sethi @ iwillteachyoutoberich.com

Google for their most recent stuff. The best promotion changes on a week-to-week basis. It's, again, really, really not worth your time to chase it given that you could be running a software business instead.