All towns on the map have a base population and towns grow based on a percentage on top of that. The higher a town's base population, the easier it is to get to 1500 people.
Things that make a town grow:
1. Public transport destinations. Connect as many towns together with public transport as you can. Passengers will change over to other lines up to a certain time limit, so the faster you can get people from point A to point B, the further they will be prepared to travel.
2. Road connections. Feels counter productive since you're running a transport company, but you also want to make sure that towns have proper road connections between them. At the start of the game all towns are connected with basic small country roads with low speed limits. Some towns aren't connected at all! Roads are dirt cheap, so upgrade all those roads to medium (4 lane) country roads with the max speed limit so people can get around must faster. Again, time is a factor, so higher speed limits mean people are prepared to go further.
3. Cargo supply. All towns require two specific cargo types to be delivered from the various industries around the map. Supply needs to be ongoing in order to keep the growth boost.
Things that make a town shrink:
1. Overcrowded stations. Generally people are happy to wait for the next bus or train for quite a while, but when stations start to overcrowd you'll get a penalty to town growth. Make sure your lines can handle the number of people that want to use it.
2. Traffic jams. I've never seen this become a major issue as long as you give people enough options to get from A to B. Make sure roads are wide enough to handle the traffic and keep an eye on busy intersections. If you see a lot of traffic going in a certain direction, check the destinations map layer to see where that traffic is going and consider building a passenger line to turn that traffic into money.
3. Emissions. By far the biggest issue you'll deal with. All vehicles, from diesel buses to electric trains to airplanes, cause emissions. Poorly maintained vehicles cause more emissions, so part of the problem can be fixed by throwing more money at maintenance. Also, only residential buildings seem to be affected, so if you can keep your busy rail lines and airports away from residential zones it will help a lot. Generally you'll want to fix the emissions after you sorted out the cargo deliveries, as it can only really be dealt with once you have plenty of income to pay for maintenance.