This answer assumes that a terraformed planet allows establishing a self-sustainable settlement on its surface without the need for special protection such as domes or special suits. In other words, once a planet is terraformed it becomes Earth ver. 2.0 with some small but insignificant changes.
With your conditions, Mars is the only option potentially suitable for terraforming:
- it is close enough, so we do not have to spend years (or centuries) travelling to it before we can establish an FTL gate;
- it is big enough to hold an atmosphere;
- it has easily accessible (but frozen) water;
- it has a continental-like crust;
- it seems to have no life presently.
- Mars is cold (perhaps can be fixed with an atmosphere and controlled greenhouse effect);
- its gravity is only 38% of Earth's, which leads to not well-understood health consequences;
- it is not clear how low gravity will affect our ability to produce food in a long run;
- the tectonic activity is either dormant or non-existent for a very long time;
- it has no magnetosphere (theoretically can be fixed with a big electromagnetic shield);
- there is a remote possibility that as we revive the planet we will encounter potentially dangerous prions or primitive life.
With the current or slightly higher level of technology, your main challenges most likely would be related to transporting raw materials to Mars to create a breathable atmosphere and topsoil essential for establishing an Earth-like ecosystem.
Ecosystem itself will be an enormous undertaking, and I am not sure it is possible to achieve a somewhat balanced state in a period of several decades. You will need just the right mix of bacteria, plants, insects, and whatever else you want to be there for the system to function properly and not to collapse. Even if we have enough processing power to model an entire eco-system, we do not know enough for the model to be very accurate. Therefore, we'll be forced to resort to a combination of modelling and trial-and-error approaches. It takes time. Or we might get lucky :)
You will also need to build, man, and maintain an extensive network of observational stations that will monitor the world. They will be necessary to make sure that everything is balanced. The collected data will be invaluable for terraforming tweaks (if necessary) and early warnings.
From what I read no other planet, moon, or asteroid in the Solar system can be terraformed with modern or near-future technologies. (Protected settlements are possible, though.) So, they are off the list.
Planets in other star systems are just too far away and do not fit into your timeframe. They might be very much like our Earth and require minimal changes, but just travelling time to them is enormous. You might get to them faster if you wait a century for more advanced space travel technologies.