If participants will be assigned to the control or treatment groups randomly, this is a run-of-the-mill experiment (not a quasi-experimental design) and you can use all of the usual statistics. On the other hand, if the control group is really a bunch of people who did not qualify for the intervention or were excluded by you or someone else based on some other criteria, then what you have is indeed a quasi-experiment.
Of course, if people registered voluntarily to participate in the study or were screened beforehand, its generalization to a broader population is open to discussion (as are all clinical trials in fact) but the “randomization” part in introductory psychology research method texts usually refers to treatment assignment, not to the fact that the participants form a random sample of anything. The difference therefore does not lie in the type of sample (random or community sample, treatment sample, convenience sample) but in treatment assignment (who goes to the control and who gets the intervention).
If you want more specifics on the analysis you will need to post a lot more details about the study (perhaps in a follow-up question).