I also wouldn't advocate adding gears to a single speed bike; it's unlikely to be economical and is unlikely to give as good a result as buying a geared bike. This related question has some other ideas in the accepted answer, but probably don't count as budget.
Looking on Decathlon's Indian website, they sell road bikes with Shimano Tourney derailleurs and also Microshift, both good budget options. They also sell hybrid bikes with Suntour and Microshift components. Some of these look a little outdated compared to the high end products these companies also offer, but I don't think this means they are any less reliable.
These are all established brands, recognised worldwide and with reputations to maintain - they should be reliable parts or have reasonable support from the manufacturer if problems do occur.