This is a question that is often asked as users are sometimes confused to what may be the best option.
If the forklift is working mainly outside then diesel is a good option as a diesel engine generally has good torque characteristics and they also come in larger sizes i.e., up to 50 ton lifting capacities. This is not the case with electric and gas-powered forklifts generally. The diesel emissions are of less concern as the machine works outside and not in a closed environment. Diesel is also relatively cost effective when compared to LPG.
If you are going to be working indoors then LPG is an option if electric powered forklifts are not possible. LPG forklifts are however relatively expensive to run in respect of fuel costs and are not as torquey as their diesel counterparts. Their emissions are however less harmful than diesel derivatives.
The best option for indoor use is however electric (battery powered) forklifts. They have zero emissions and contribute very little to noise pollution as they are quiet. While the initial capital outlay may be marginally higher than an internal combustion forklift, the cost of ownership is lower over time due to a zero-fuel bill (apart from charging the battery).
One now also has the option of Lithium batteries which have many advantages over traditional lead acid batteries i.e. zero maintenance, opportunity charging is encouraged, longer life span, shorter charging times, etc.