Which is the best type of lawn mower for me.?
I just have a small yard. I love the feel & weight of the electric ones I used when I was a kid. I am put off by the new cordless ones because of high-cost. I would also like a push-powered one as I understand they are much more efficient than in the past. I'm a small rather weak man so it would have to be more efficint than in the poast.

The cordless electric mowers are expensive and heavy.
My first reccommendation would be for you to find a good local Honda dealer that will service what they sell. If they also sell Harleys… don't walk away… RUN!!! Barring a Honda dealer that also does service… find someone that does work on Honda's. Then… buy a Honda!!! They are not cheap, however, my Honda is 24 years old. It looks like crap, smokes, and is a bit noisy… but… it wasn't always that way for alot of those 24 years, and it still starts on the first pull every spring. The newer ones have plastic decks, are super light and have great power to weight ratios. They are a bit expensive, but not if you consider that you are likely to own it for 2 to 3 decades.
Secondly… don't rule out the old-fashioned push reel mowers. If your property is small, you might just be able to handle the new models of reel mower… they are not like their old cousins anymore… they spin faster, stay sharp longer, and are made of lighter materials. Plus, they never need oil, gas or expensive repairs. Properly maintained… you'll buy one before someone buys you a casket… sure, some might say that pushing one of those around will put you IN a casket faster, but, then, NOT pushing one around might too…
My two cents!
You don't mention a sloped yard and said you are "small and rather weak" so a ride-on mower seems like a good option. On the other hand you also said your yard is small and you are drawn to push-behind models.
From a purely environmental perspective, the motorized push-behinds are horrid in terms of emissions. I read somewhere that a lawnmower running for an hour emits as much as 500 cars. Whether or not that's 100% accurate or not it does give you an idea how nasty they can be.
The electric mowers are quite efficient and easy to maintain and much kinder on the environment. Also, given you have a small yard you shouldn't have to worry about the battery charge running out on you. You might want to look into self-propelled models to help you with the pushing.
With a smaller yard you probably don't need to be as concerned about a wide swath but it is something to be aware of while shopping around.
As far as brands, there are many quality ones to choose from. I have personally had a lot of luck with Husqvarnas.