If you have a posh lawn the answer is simple, a cylinder mower with a roller to put the stripes down. Best to have a full time gardener as well. For most typical home gardens a rotary mower is sufficient, and then the choice is between an electric or a self propelled petrol mower.
A small electric rotary mower, or even a battery powered one, will work for a small area of grass. The bigger the grass area the more cumbersome they become when used, with long electric cable lines just waiting to be cut. Be sure to buy an RCD (Residual Current Device) to protect you from this, and do not cut when wet.
Electric mowers come in a variety of sizes to suit most lawns. Stick with a well known brand and you will be good to go. I find electric mowers whilst cheap tend to last only a few years until the engine burns out.
For the larger lawn a self powered petrol mower is preferred. You need to be careful when buying at the cheaper end as those are built to a price and may be of poor quality. Having hired a certain brand of mower for several years I bought one as I thought they were a good make. The one I bought was cheap and nasty. The brand had been sold and the mechanics and design of the mower were not thought out. It only lasted four years. I was given an older one of the same make which was much better thought out and had better parts. It has had a full refurbishment and is likely to last another 10 years plus.
Before buying a petrol driven self propelled mower read the buyers reviews, and better still if you can see one close up to determine its build quality. A good mower will cost more but will last longer and do a better job. Be sure to have it serviced regularly.