What is the best way to carry it home?
1) Remove the packing box, wrap the projector in some clothes and carry it in the cabin baggage.
I've always travelled by Emirates and Air India from the United States, hand baggage rules are more or less similar. The dimensions allowed are upto 22 x 15 x 8 inches (55 x 38 x 20cm) and weight upto 7kg. Measure the dimensions and weight of your packed up (in original packing) projector and ascertain if it falls within these limits. If it does'nt from a size perspective, reduce the size of the packaging. In my opinion, it is always better to have the original packing because you will have to place your projector in the over-head luggage compartments, which are usually jam-packed with stuff. The original packaging will offer some protection, especially when the aircraft inclines during take-off and landing.
It would look odd if you wrap the projector with clothes and carry it :lol: You'll have to do this right through the airport, customs, etc and you'll definitely trigger off a lot of smiles on the way.
2) Do the same but put it in the check-in baggage
If you do so, ensure that the projector is properly packaged (possibly with a double box approach). Pad up for both impact caused by throwing and weight resistance (baggage may be stacked). In my opinion, don't use this option unless absolutely necessary. It is better to check the equipment in, with its original packing or an additional outer box packaging but you'll tend to attract un-wanted attention when you roll your trolley about the place with electronics stacked up (especially with customs). Baggage handlers at airports tend to handle checked in electronics in original box (with a fragile sticker) with a lot more care but there are no gaurantees.
3) Keep it factory packed and carry it as a cabin baggage
Please refer to my reply for point-1
4) Keep it factory packed and put it in the bag for check-in baggage
Please refer to my reply for point-2
5) Any other option
Shipping is the other option, risky and expensive (and will also attract customs duty, courtesy, Indian customs)
I have hand carried turntables from the United States, packed in their original factory box packaging. Brought them home safely. Have also hand carried LP records both wrapped in strong pager and also in a small box. Again, reached home safely.