Air Guns are a great way to get started in the field of target sports, and can help improve concentration, hand-eye coordination and can generally be a good stress reliever! 
While imported airguns can be a bit expensive due to high demand and indirect/ unorganized means of procurement, there are a range of options manufactured within the country that will suit all budget needs and allow you to have endless hours of fun without burning a hole in your pocket. A few economical brands in air pistols are Sisco, He Man, Batman, Hawk, Tommy, Daws in mostly smooth bore but reasonable power for paper, cardboard targets and tins. Mid-range brands include SDB, few models of He Man, Globus and the like, while IHP and Precihole (recent) are the high performance brands holding their reputation in the market consistently (both air pistols and rifles alike). UTA, GD Sports, Daws and Gift Industries make cost-effective rifles of reasonably good quality and are available at local stores and online without difficulty. 

Working Mechanism
Most Indian made air guns are based on break-barrel, spring piston mechanism, while a few brands have introduced PCP pistols and rifles recently (IHP, Aditya Innovations). 
Within the break-barrel design, the under lever mechanism is now gaining popularity among a few brands like the AK 550 Under Lever Rifle, and the Under Lever Air Rifle by GD Sports 

Licenses/ Legal
While there is a constant row between airgun enthusiasts and opposers due to the safety debate, Air Guns are officially exempted from the Arms Act 1959 as they are classified under category GSR 991 goods for sports. Technically any air gun that has a muzzle energy of lower than 20 joules (recently changed to 15 joules) or of 0.177 caliber bore (4.5 mm) fall under this category and hence do not require a license. Since all indian-made airguns conform to these regulations (usually) they belong to this category.  However, import of airguns into the country is regulated by the government and requires the importer to fulfill certain legal formalities before one can own these. 

Air guns (both pistols and rifles) are prohibited from being transported via flights due to airline regulations and are therefore always transported by surface.