Yes, you need the machine, and the basic package should include SlimLine tubing, the power supply, the humidifier which is built in, the SD Card, one filter, and a travel case. Some places will put together a few more things in a package, such as extra filters, the heated ClimateLine hose, and sometimes a choice of a mask from a limited selection. These can be a good deal when you add it up. Even if you have to buy it as an option I would recommend the ClimateLine hose. It does add to the comfort factor, and makes it easier to get the humidifier setting right. Some like to add in the SoClean machine and I think that is a bit of a scam and not worth it. Distilled water you can get from places like Walmart etc.
On the prescription I doubt that anyone would prescribe any specific mask, and you wouldn't want them to. I would think just a prescription to use a CPAP is all you need. Perhaps call a vendor you are considering using to ask what they want for a prescription. I suspect what that site means by saying they need a prescription to buy a mask, is that they are making the point that you need a prescription for a CPAP to get a replacement mask. It seems to be a goofy US rule. It is not a requirement in Canada. You should not have to get a prescription for each mask you buy. Perhaps if you can get as bonjour suggests just a prescription for the APAP and mask of choice you will be good to go.
On the mask, if you just have to pick one without trying it ahead of time, I would pick the ResMed Swift FX nasal pillow, or the ResMed AirFit P10 nasal pillow. They are two of the lower priced masks and typically get good reviews for comfort. The head straps on the P10 are somewhat flimsy and are not that durable, and can have issues with keeping the mask in place. The P10 has a very quiet exhaust port though. The headgear on the Swift FX is more substantial and I suspect will last longer without replacement. The Swift FX exhaust port is not as good as the P10 but it can be worked around. I've used the P10 for about 9 months now, and have just replaced it with the Swift FX. For either one if you are just buying them on line make sure you get the fit pack version. It includes three sizes of nasal pillow inserts.
They both come in standard and For Her versions. I would buy the standard if you are male, and the For Her if you are female. In both versions the nasal pillow inserts for the standard version are small, medium, and Large. In the For Her version they are extra small, small, and medium. The headgear on the Swift FX For Her is a bit smaller than on the standard. On the P10 I believe the headgear size is the same on them both. It is very elastic, and part of the reason why it is kind of flimsy.
Hope that helps some,