If you're feeling slippage in the clutch, the only minor action you can take is to go easy on it until you can replace the clutch or get it replaced. A clutch can start slipping for a few different reasons, but would suggest 150k miles is not insignificant and your clutch is just worn out. Ultimately replacement is going to be your only real recourse.
In your question, you had several thing which you are unsure of, so would like to address them.
First, yes, your clutch should be self adjusting. More than likely, it has used up all of its adjustment area and it's now just living on borrowed time.
Second, having to depress the clutch pedal hard to the floor would be unrelated. I'm assuming the deal is, the engine won't crank at all unless the pedal is hard to the floor. There is, on most manual-shift vehicles, what is called a neutral safety switch. When you depress the clutch pedal this switch is engaged, which allows the starting circuit to complete allowing you to start your car. This isn't a problem with your transmission or clutch, but rather is probably just the switch needing to be in adjusted so you don't have to cram it to the floor. This can also happen if you have a thick floor mat which the clutch pedal comes down on. This can make it feel like you're ramming it through the floor, but in actuality, it's just the mat which is not allowing it to go down all the way.
Thirdly, most likely you'll not need to get any work done directly to the transmission. You'd only need to get the clutch replaced. The clutch and the transmission are two separate entities and perform two different jobs. Don't let that fool you, though, as you have to remove the transmission in order to replace the clutch. This means if you're not doing the work yourself, there will be a bit of labor involved in getting it replaced. In most small front wheel drive cars, it is actually easier to remove the engine and transmission as a unit, then separate them "on the bench", reassemble and then put it all back into the car as a unit. It's just easier than trying to work around body panels and such.
One last thing to consider is your replacement options. When you replace your clutch, it is my opinion your best course of action is to replace the clutch, flywheel, and throw-out bearing all at once. You'd, at the very least, need to resurface the flywheel. This isn't a big deal and doesn't cost too much money as long as the shop which does the work can do it on sight. Most shops these days do not have that capability, so have to send it to a machine shop to have the work done. This takes time. Getting an entire clutch kit saves a lot of time and effort, and really shouldn't cost too much more money than resurfacing the old flywheel. Plus you have the added benefit of knowing you have a new flywheel which should have zero issues. As far as the throw-out bearing, consider it a maintenance item and replace it without thinking about it. The cost of replacing it now versus having to replace it down the road and paying labor fees again to get it done should give you ample reason to do it now.