The biggest difference between home theater and business use is going to come in the form of contrast vs. lumens and projector size. The bottom line is that home theater projectors are designed completely differently than business projectors, even if they sometimes use the same DLP or LCD chips in them.
Home theater projectors are typically not very portable. They use their increased size to cut down on noise from the projector. So, they tend to be quieter. They are often not as bright because it can help with contrast, decrease cooling requirements, which lowers noise. They often have higher resolution and typically are 1920x1080 resolution which matches the HD aspect ratio of 16:9. Finally, they have a much stronger focus on image processing and performance with video, including accurate color, shadow detail, motion handling, and contrast.
All that said, if your primary use is business, and you are hoping for the occassional home use, then I would focus on getting a decent portable business projector. I would stick to LCD and would get a model with 1280x800 resolution or higher, but always widescreen. No 1024x768 projector makes sense anymore.
So, while I would strongly recommend a projector for home theater as a great choice, they just aren't really portable. A model from this list (sorted by popularity):
http://www.projectorcentral.com/projectors.cfm?g=1&hide=0&st=1&r=&br=&c=&w=&ar=Wide+(16:9-10)&db=&zr=&wt=<g=&ll=&mfg=&p=300&p=3000&wr=&dt=1.0.0&t=&pjl=0&pjw=0&pjh=0&td=&is=&i=d&tr=&tr2=&oop=2&sort=pop&sz=15
Specifically the Epson 3700:
http://www.projectorcentral.com/Epson-PowerLite_Home_Cinema_3700.htm
Is great. It's got really great brightness, solid reviews, good contrast, excellent placement flexibility...
and it weighs 15 pounds. About twice what a heavy laptop comes in at! Not really portable, but that's absolutely my first recommendation for a solid home theater model which could double for business use.
Now, how much light you want to deliver on screen and need for the projector will impact size, price, noise level, and image quality. In a business setting you want no less than 50 lumens per square foot of screen space. That will be no less than 80 advertised lumens per square foot. A typical screen will be about 44 square feet for a 120" diagonal image. So about 3,500 lumens is recommended for the projector rating (hence, the Epson 3700 is a great choice).
But, more lumens is still much better in a business environment where lighting often can't be controlled.
A very bright model which is well priced for the brightness is the Epson 2250.
https://epson.com/For-Work/Projectors/Meeting-Room/PowerLite-2250U-Wireless-Full-HD-WUXGA-3LCD-Projector-/p/V11H871020
At 10 pounds it isn't exactly the most portable unit, and likely is overkill. Also, the $1,500 price point may be more than you are looking to spend.
I think if I were buying right now, and wanted the most bang for the buck overall, and would be happy with about a 100" diagonal in the business space, then this would be a great option:
https://epson.com/For-Work/Projectors/Portable/EX9200-Pro-Wireless-WUXGA-3LCD-Projector/p/V11H722020
At $700, you get full WUXGA resolution (1920x1200) and 3,200 lumens of brightness from a 5.7 pound projector. Pretty solid!
If you want to up the portability, then this model really nails it for a bit more cash:
https://epson.com/For-Work/Projectors/Portable/PowerLite-1795F-Wireless-Full-HD-1080p-3LCD-Projector-/p/V11H796020
This is a true 1080p projector (1920x1080) which is still 3,200 lumens, but comes in at only 4 pounds. It's also built super flat to fit into a typical computer type bag easily. A large computer bag could easily carry the projector and a laptop together.
Finally, if you are like "Dude! Can you show me something really cheap?"
Yep:
https://epson.com/For-Work/Projectors/Portable/VS345-WXGA-3LCD-Projector/p/V11H718220
This is 3,000 lumens, and is 1280x800 resolution. It's a solid starting point for front projection and while it won't blow anyone away, it will get the job done and still be fun for some home use.
Also, on the 'budget' side, check out their 'refurb store' for some price savings:
https://epson.com/Clearance-Center/Projectors-for-Work/c/cc302
Where you can get a WXGA (1280x800) 3,000 lumen projector for under $400.
https://epson.com/Clearance-Center/Projectors-for-Work/EX6220-WXGA-3LCD-Projector---Refurbished/p/V11H550220-N
or even get a WUXGA model (1920x1200) for 560 bucks.
https://epson.com/Clearance-Center/Projectors-for-Work/EX9200-Pro-Wireless-WUXGA-3LCD-Projector---Refurbished/p/V11H722020-N
So much depends on what you are really shooting for here as personal preference. Even with so much focus on Epson, Panasonic makes some great widescreen options which will work as well, along with Sony and a few others. Epson just has well known support if you need it and often has some lamps which can be very fairly priced which is nice as replacement lamps can run $250+ for factory branded models.