The game tells to buy special weapons but the gems are not enough to buy them. So what are the other..

Unless you really need the special weapon, don't buy it. Or alternatively if you do have a shitload of gems and need a special weapon buy it. I think I cashed gems in once to buy a weapon. But remember that weapon is usually only good enough for about 2 levels anyway. So for me just buy the basic weapon required for each level. Trick it up to max and you will be fine. The other trick I used was to get good assault rifles. They are particularly good for helicopter and overhead burglars etc. They are expensive but worthwhile.

Buy shotgun most of the time. Is the easy way to complete all preliminary tasks.. and shotgun is best for world ops play..