To maximize earnings you're going to want to get to elite status as quickly as possible. Given this, there are two good options I am aware of:

AA Status Challege - Will get Platinum after 10,000 Elite Qualifying Points, if I'm understanding your post correctly and your company pays for domestic first class, this should happen pretty quickly. AA is a good program to accrue miles in general, redemption is pretty easy. If I understand you correctly that your company pays for first class I think this is the way to go. Cost of this is $125-$150.

US Airways Try Preferred - US has a program they usually have, but it doesn't appear to be on their website right now, called "Try Preferred". They may have discontinued it, but it's just as likely it's a beginning of year issue or new website issue (they recently launched the new website), so you could try calling and asking about it. You would get Silver and then based on your elite qualifying miles flown during the 90 days after you sign up, you can read some discussion of it at the bottom of the first post in this thread. Cost of this is about $200.

I would definitely go with AA, just wanted to give you another potential option.

Right now for hotels, Hilton (which includes Hilton and Hampton) just announced their Q1 promotion and it's good, 1 free night at any property after every four stays or 10 nights at nearly any Hilton Family hotel (see thread for excluded hotels, 37 hotels are excluded, not that many actually). You can also double dip with Hilton, earn hotel points and airline miles/points, if you do that I would actually suggest taking the airline miles in Southwest Airlines (which is also the best program to credit rental cars to also).

Hyatt Hotels has an excellent promotion (The Next Big Thing) that runs through the end of January if you can use them.