Most commercial van conversions aren't very stealthy.
Would it be cheaper to buy already converted? That depends on the asking price. I've had friends who have bought very old, high mileage camper conversions under $5000. Vans from the early 1990s for sale today have asking prices ranging from $3500 to $20,000 (those at the upper end were probably over $80,000 when new).
How much it would cost to buy a used cargo van and have the work done depends on that van market and just how much you want done. A used 10-15 year old E-250 with over 200,000 miles sells here for about $6000, a five year old van with that mileage about $9,000 while a 2011 E-250 with less than 100K miles runs $15,000 dollars. Demand for usable E-series vans has become quite high since Ford stopped making them.
Then there is the cost of conversion, which depends just how much you want to put into it. Typical camper conversions from shops that specialize in this (like Sportsmobile, but there are many smaller shops) put about $30,000 materials and labor into a RV-quality conversion (e.g. includes bathroom and cooking facilities). If just cabinets, beds, some seating, and windows with screens, you might design a minimalist package in the $12,000 - $20,000 price range (Sportsmobile has component by component price lists on their web site).
There are enough van conversion companies out there, I would not consider looking for a carpenter who might not have the experience to plan a conversion that will fit your living needs. Look into Sportsmobile, Van Specialities, Craftsman Vans, GTRV for experienced builders.
I don't think you are going to get anywhere near $16,000 even if you started with a $5000 cargo van and found a really inexpensive contractor. There are possibilities for DIY, if you don't really need cabinet work, and can find used fixtures. There are a number of sources for DIY information, from building slide-in packages all the way down to "turn your minivan into a camper using old milk crates.
But $16,000 can probably get you a fairly nice 20 year old B motorhome.
Tom Test
Itasca Spirit 29B