Really depends on use and practicalities.
Where are you going to store it, for example - if in garden shed either electrical or petrol, but if in house anywhere definitely not petrol (smell, risk, etc). I've had both over the years, personally I prefer petrol as it avoids hassle of leads and is better at cutting longer grass. With electrical mowers they struggle if the grass is not cut as frequently, so I find petrol ones a bit more flexible from that perspective. Also petrol ones I find a bit better if grass is a little damp.
You also mention a second house/lawn. When cutting grass there do you have easy access to power (eg if a rental house is there any hassle getting in for power, if so petrol may be easier). Though electrical much easier to transport in a car boot, lighter and generally a bit smaller. Also if you don't have a side passway and had to take through the house electric is definitely easier.
Re battery operated - never had one, but had battery strimmer. Great at the start but after one year I found the battery life terrible and one full charge would not do each time. No idea if same applies to mower but reality is you need strength in a mower.
I would tend to look at the practicalities and use, rather than purely price, as mowers last, if minded, as a one off type purchase.
Woodies have tended in the past to do Easter sales with decent petrol mowers around the one fifty mark. A good electrical one would be in the same price range. Don't think brand name is that imporant unless you want to spend a lot more.