Actually, your 737 was making money, but because you had the 707, you in general made losses (operating the 707 cost uyou more money than you got from 737). So, you can start with bigger aircraft, but you have to make sure that it doesn't consume too much fuel (about 5000kg/hr max). When choosing an aircraft, the most important things to consider are:
1.) what kind of route it will fly (short, <1000nm -> use turboprop; medium 500-2000nm -> small jet (ERJs, Bombardier) or medium jet (B737/A320/321); or longhaul 1500nm-6000nm -> big jets (B747/757/767/777/A330/A340/DC10/MD11/Tristar)). Always check that the demand for the route is more than what the airplane is capable to take on board with the current configuration. If there are many routes to choose from, pick the one with highest F/C demand (will give more profits after you reconfigure the aircrat to include those classes).
2.)How many passengers it's able to carry.
3.)Fuel economy. Depending on aircraft size, but it's usually good to compare many same-sized aircraft, and see that the plane you chooce doesn't have the highest fuel concumption.
4.)Price. Important, when there's the chance to get 2 airplanes of the same type at start.
5.)Aircraft age/condition. Age should be no more than 10-12 years (but for the first aircraft, not less than 4years, it's just not worth the money you need in the beginning. Aircraft condition should be no less than 70%. Again, the higher, the better, but no need to get aircraft with >90% condition, because it's not worth it. Only, if there are no other aircraft of the same model available, should you take it.
6.)Aircraft and Engine type. If you are choosing your 1st airplane, doesn't affect. But, when getting additional planes, you should always get the same model and engines, as the airplane will then be cheaper to maintain. So, if you have a 737-300 with PW engines, try to get another 737-300 with PW engines. if not able, try other engines. If again not possible, get at least a 737 (fort example -400). Only, if you just can't get another 737(because there aren't any on the market; or, you need a totally different type of airplane, a turboprop for example), choose another aircraft type. But, again, chooce a type you can use later and can get more than one when needed, so you don't have 10 different aircraft, all different types.
7.)Speed. Not that important, but the faster the plane goes, the longer you fly in the same amount of time allowing you to fly longer in a single day, or make 1 extra flight every day, both increasing your income.
8.)Range. Always make sure your aircraft is able to fly the route you want it to fly. it's not good to make a jet fly a long route with the capability to take only half the passengers on board -> you make less money.
9.)Turn around time. The less time the plane stays on ground, the more time it will have to fly. And when aircraft flies, it (should) bring you money. Of course, when creating a route, you should put the rutn around time longer than the minimum, otherwise there will be a lot of cancellations, which affect your image and income. Usually it's good to put the propability under 10% (but on 0% only, if you don't need the extra time to make another flight).
I think those are the most important ones. You may not always have to think all of them, but it's good to know how each of them affects.