Both air purifiers and indoor air quality monitors serve a useful purpose since most air purifiers aren't able to monitor carbon monoxide, radon and particulate matter levels. If you are forced to pick one or the other because of your budget, your best bet is getting an air purifier and cut to the chase since it's likely you will need one anyways, after monitoring the indoor air with an air quality monitor.
When choosing an air purifier, you want to keep in mind functional features and size since an air purifier that is too small for the job will take much longer to clean up the air. The Proscenic A8 is a good choice of air purifier because of its 220 cubic meters per hour (m3/h) airflow rate, which means the Proscenic A8 air purifier can circulate room air over 3 times per hour. Proscenic states the A8 purifier can service a room up to 430 ft² (square meters) or 40 m² (square feet).
The best way to calculate whether the A8 purifier will be suitable for your needs is by using the following airflow rate formula, which consists of multiplying the room dimensions by ten. For example, if your room is 3 meters wide, 3 meters long and 3 meters high, the calculation will be as follows (3x3x3) x 10 = 270, which translates to 270m3/h.
The Proscenic A8 air purifier uses a H13 filter, which isn't just a high-efficiency particulate air (HEPA) filter. It also integrates a pre-filter layer, a nano filter layer and an activated carbon filter layer, all of which contribute to improving the air quality. A HEPA filter alone can only remove dust and allergens (i.e. mold), while a carbon filter can filter out cigarette smoke, fumes and other chemicals.
A replacement H13 filter can be bought from amazon, although you could potentially use a third-party alternative if you can find a cylindrical HEPA air filter that fits. The Proscenic H13 air filter measures 18cm tall and has a 9cm diameter. Weighs 222 grams.The user guide states the Proscenic H13 air filter is rated for 2000 hours of operation, while Proscenic also recommends replacing the filter every 3-6 months, which seems a little confusing since the 2000 hour rating actually translates to 84 days. If you were to use the Proscenic A8 air purifier for 1 hour each day, the filter would technically last 2 months and a half (84 days). 
If you were to run the Proscenic A8 air purifier for 3 hours every day, the lifespan of the filter would technically be 28 days. The likely reason for the A8 air purifier 2000-hour rating is because a regular HEPA air filter can last up to 12 months, whereas a pre-filter and carbon filter have to be replaced between 3 and 6 months.