Petrol lawn mower for big garden

Found this forum looking for lawn mower advice so here is my first post.
My garden is about 3 tennis courts plus a bit more at the front. Some areas a bit uneven, so assume rotary isbedt option. I want self propelled but from using a friends cheap one I realise some are less propelled than others.
My old Honda is about had it. Please tell me what I should be looking for in the replacement. Engine size? Make? Features? Any advice is appreciated as the prices range from 150 to over 1000.

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