You'll find SSRs widely recommended here and in other places with a lowish skills base, but they are by and large ignored by more advanced engineers. They look attractive to the hobbyist - they have the ease of wiring and isolation of a relay but the speed of a semiconductor, and no need to calculate component values as you would for a transistor. However, in reality the downsides tend to be greater than the advantages so SSRs tend to be the mark of a noob.
Biggest of these is the sheer cost. I don't know exactly what kind of motor you were controlling but consider something fairly average for that kind of problem - 12V and 2A. Controlling that with a power transistor would cost around 60p in components here in the UK. Using a mechanical relay may cost £1.50. A suitable SSR is likely to cost well over £20.00.
Using a power transistor means a suitable type needs to be selected and component values calculated to suit. However, most electronic engineers have a mental listing of perhaps 10-20 different transistors that they are very familiar with and can simply select an appropriate one from those in the blink of an eye. You need to calculate a resistance for the transistor base which can be tricky for those without the required understanding but it is a matter of 10 or 15 seconds with a calculator for someone with experience.
Using a mechanical relay reduces the skills needed to make a working design but at the cost of speed of response. On the plus side it will remain a lot cooler. The losses in transistors tend not to be high as a proportion of the power handled but they can be enough to create cooling issues. Losses in a relay are orders of magnitude lower so the relay remains cool.
Using an SSR firstly you have to pay for it as has already been mentioned, then you design it in as for a conventional relay. However, you have the same heat issues as you have for transistors.
In practice I suspect I would probably opt for a combination of relay and transistor for this kind of project - use a relay to reverse the direction (it's easier than using four separate transistors) with a single transistor to turn the motor on and off. A transistor's switching speed allows for speed control even from a digital MCU output by means of pulse width modulation - essentially turning the motor on and off rapidly. You can't do that with relays.
On a more general note the kind of people that populate hackerspaces are in general a helpful bunch but you need to approach them with the right mindset. If you ask this kind of question people will be only too happy to explain but you will not endear yourself to them if you conduct yourself as if you have equivalent levels of expertise to people with greater skills in an area. As such it's best to ask this kind of thing there and then - you'll look far less foolish in the long run.
One final point about the voltages that the earlier respondent alluded to: there is certainly some truth to what he says although the maximum working voltage of any SSR I have ever seen is well below what you can do with a relay. In addition you need to be wary of considering motors or other inductive components purely as low voltage devices - a 12V motor may generate ten times that voltage internally and may output that voltage to the circuit as brief transients in certain conditions. This is why you need the suppression capacitors to control radio interference as sparks literally fly as a result of those voltages. Those voltages can certainly damage a transistor or even an SSR if they are above the rated voltage for the device. Mechanical relays are a lot more forgiving in that respect.