Does this model come with it's first filter, or do I have to purchase seperately?

Yes, it does come with its own HEPA filter. However, when I replace mine I just buy one of those HVAC home 12 by 25inch pleated filters from Home Depot to replace them with. They are much cheaper and do a good job.

Would this be good in an office enviroment to put on my desk to eliminate cologne and perfume smells?

I realize this question is a couple of years old, but for other potential buyers--I've been running this on my desk on high for over a year and have never had any comments or complaints from callers. It's next to my laptop and appx 1.5-2' from me, and I've never had any issues. I don't have issues with strong colognes or perfumes, but the air in my home office is always noticeably fresher than the air in the rest of my home and I have open windows/moderate-heavy pollen most of the year. (I'm here now for unit #2.)

Is this good for smokers?

The HEPA filter will remove quite a bit of smoke but it won't last near as long in a smoky environment, Using the ionizer might be a bad idea for smokers. The ionizer will change the smoke into a substance that will stick to everything more vigorously than usual. The odor from the remnants of ionized smoke is sticky and more pungent after it has collected on nearby objects over time, and it's MUCH harder to wipe away.

how often do you have to change the filter?

We live in rural northern Alabama where there is a lot of pollen and cotton/corn fields; 6 to 7 months is the maximum we can go on a single filter. We use the HAPF300AP-U4 filters which claim to last 12 months but air flow is significantly reduced by 6 months; going any longer would probably put an unnecessary strain on the motor and shorten the life of the purifier. My children have severe allergies; so we immediately know when the filters need to be changed.