Hi there,
Good number of questions! Nice and meaty to get my teeth into! Ok, here we go...
That the planets appeared as white/brown disks in a small scope to me says that the scope is either poor quality, or too much magnification was being used. Leaving the quality of the telescope aside, there are three things that govern the image quality:
1) quality of the eyepieces;
2) the maximum magnification that a telescope can provide- there is a rule of 50X per inch of apeture, for all telescopes, beyond which the resolving capability of the optics degrades. So if your scope is only 2", its max. practical power is 100X, if it is 10", then 500X is its practical max. limit.
3) the atmosphere- here it doesn't matter how big your scope is, the conditions of the atmosphere is the single biggest limiting factor, and it doesn't matter how big your telescope is. Normal conditions limit the magnification to between 100X & 150X. Rarely is more possible without the image quickly degrading, say like 300X. Anything more requires very careful observing site selection- ever thought why professional scopes sit on top of tall mountians? As an example, I've only been able to get a good image at 330X with my big 17.5" scope three times in the last year, not excellent, only good.
The other thing that governs the comfort of viewing the moon and planets is that they can be really bright, especially the moon. If you only get one filter, I would suggest a polarising filter set. These are two polarising filters that you then use to vary the amount of light getting through. When I do view the moon, this is what I use.
There is an astro retailer here in Sydney that sells these polarising filters for $19 each. Purchasing two will make this polarising filter set. Look in the heading of "Guan Sheng" towards the end of the page is the filter selection:
http://andrewscom.com.au/site-section-10.htm
Under the "General Accessories" is a selection of inexpensive colour filters. The link to the Lumicon filters is not intended as an advertisement for them, but to show you what the various filters are designed to do and what they will help show.
A scope of the size you are looking at, 3 or 4", is still good for DSO's in the city. I live in Sydney, so my sky too is very light polluted. I started with only a 2" scope, and learnt how to make the most of things with it. I often observe with my 5" scope from home, not just with the17.5" as the 5" is really quick to set up. Open clusters, globular clusters, and bright nebulae are still observable, even from Jeddah City,
. There is even a number of galaxies too that are within the range of scope you are looking at, from a city observing site.
The main thing is to try to shield the site you are observing from, from strong direct lighting, like street lights and the neighbours flood lights. This alone will improve things imensely. This will reduce stray light affecting the optics and help to preserve you night vision as much as possible. A good stable mount is another to dampen quickly vibrations.
The other thing that helps is training your eyes to use what is called 'averted vision'. The most light sensitive part of our eyes is located around our central vision. By looking just to one side of the object in question, you will notice with a little practice, that fainter and more detail will be visible, and when you look directly back at the object, these details will 'disappear'! This method of viewing works in both the city and at a dark sight.
The only filters that will help with DSO's are those designed for nebulae. But because they are very selective in the spectrum they let through, they are not useful for anything else, like galaxies or clusters, as they glow across the entire range of the light spectrum. In the city, these filters do help a great deal with viewing nebulae. They can actually make a real difference in see them or not, and even identifying things like planetary nebulae from the background glow. And yes they can be expensive, but it is something then you can save money for.
You say that your eyesight might not be the best, that is not a problem. That is why I mentioned this example. My 40 year old eyes are not as good as a 17 year old's, but as I said, it is experience,
.
There is one other thing I can suggest, that is using a pair of binoculars when you are using your scope. These will allow you to see stars that light pollution rubs out when you are trying to find your way around the sky with star charts. The best thing is that it should not be hard to get your hands on a cheap second hand pair. I use mine every time in Sydney, and from a dark site, they make for beautiful wide field telescopes. The 'classic' astronomical size is 7X50mm.
Is there an astronomy club near you? They might hold regular viewing gatherings where new comers would be welcome to look through the various instruments. This will help give you an idea of what different scope sizes offer, and what good quality accessories can do. You might even be able to find a scope that someone might be selling. The folks there will be able to help answer the many questions you will have too.