Usually, Intermediates don't make any more than Basics. In most Texas systems, Intermediates are not even utilized as independent care givers, but are interchangeable with Basics. Intermediate is a very old, outdated idea that really has no place in twenty-first century EMS. The original idea was to provide a couple of critical skills for use in rural systems, where trauma victims were a long way from a hospital. Since then, we have learned that trauma victims do not benefit from those skills, and in fact suffer from Intermediates screwing around on the scene trying. But EMS is running about twenty years behind the research, so we still haven't seen the I level die out completely, even though it serves no real purpose.
If you can avoid going to Intermediate training, do so. It fragments your paramedic education and results in a lesser provider than if you went straight through a real paramedic school.
As for the fire thing, that's up to you. But you don't have just a whole lot of choices in the Houston area. Most EMS is fire-based. But there are a couple thousand people applying for each and every one of those fire jobs, so the competition is fierce, and most people never get one. Being a paramedic definitely increases your chances a little, but it's still a gamble, so you better have a Plan B. That means either moving out of the area, to some place that has real EMS, or going on to nursing school. There are a whole lot of medics in the Houston area that can find nothing but $12 dollar an hour non-emergency transfer jobs, and never even get to use the education they spent two years and thousands of dollars obtaining.