Surgical technician jobs are excellent ways to get a ton of paid clinical experience. Even at large university hospitals, you will be right in there scrubbed in on myriad cases. At a hospital with no residents, you will be second and first assisting, which can mean everything from driving the camera, retracting, suctioning, and cutting suture to actually throwing stitches, throwing ties, manipulating tissue, drilling, etc. As a regular old ST (you get the CST designation after taking one of the national exams), I've gotten to do tons of awesome stuff and have seen many cases.
The vast majority of these jobs will require at least a surgical tech certification, which is typically a 9-12 month program that covers a&p, medical terminology, instrumentation, and clinicals. At the end, you are eligible to take the CST exam. However, I have yet to meet a surgical tech who has taken it. Most jobs will say they prefer CST certification, but you can easily get hired without it.
Now, some jobs will be willing to hire you without a surgical tech certificate. These will most likely be private surgical tech jobs or very small hospitals or surgical centers. It is getting more difficult to get these types of jobs with the degree creep. Many ORs now are only hiring BSNs and LVNs. But you can typically still easily get a job as an ST if you get good experience during clinicals and sell it in your resume and interview.
As far as getting ST versus paramedic, you will have a larger scope of practice guaranteed with paramedic. You may be able to do a LOT as an ST, but it will be institution and surgeon dependent. That said, ST is easier to get into and takes way less time. For paramedic, you have to have your basic and I think a minimum number of hours in an ambulance, and then it is another year of schooling. Not sure how much paramedics get paid, but I made $27/hr as a surgical tech without national certification.
If you have any specific questions please ask!