I am a beginner of violin and I would want some advices:

1. Is it easier to do the bowing with light or heavy strings? I have been playing guitar before so the fingering is no problem with heavier strings. I am more interested to know what will easier bring the right sound.

2. In general, what is better for a beginner: nylon or steel strings? I have read that nylon is sounding like gut strings and are more preferred for classical music. I am planning to play classical music. If steel is needing less skills I will still go for steel, otherwise nylon.

3. Do you have any suggestion for beginners strings? Preferable not so expensive.

Thanks

Steel strings are more durable and more stable than nylon strings. They are generally cheaper as well. Nylon strings sound nicer (usually) an are kinder to the fingers. Some steel strings seem to be made of cheese wire. The recieved wisdom is Dominants are the best Nylon strings going, so until you are in a position to know the differencefor yourself, they are a safe bet.

To answer your questions...

What will effect getting the right sound will depend on more than just the strings. Your violin needs to have the right set up and the action (bridge distance from fingerboard) needs to be right. Then, your bow and the quality of your hair, and the rosin you put on it. Light rosin is what is recommended for the violin. Dark rosin is stickier and used more for cello and bass, because it produces a gritty sound. Then the strings. If you have bad strings, none of the above will matter because your violin could still sound like crap. (Although if the violin is just bad in general, no matter what you match it with, it'll still sound bad.) I recommend dominant strings also. Unfortunately, what you pay for is what you get, so if you buy cheap strings, they will hurt your fingers, break easily, and not sound very good. Although Dominants are about 50 dollars a set, they are a lot better quality.

To actually answer your questions.

1) The weight of strings is not relevant to bowing, but is relevant to your instrument and left hand fingers. If you hate playing the instrument, it will not sound good. The best strings tend to depend on the instrument and ultimately require experiment. A rule of thumb is old instruments require bright strings and new require darker sounding strings. Your local violin shop will give far better advice than this forum. Also a good tone is dependent on taste. Personally I like a bright tone, many prefer a more mellow tone. Only you can decide that.

2) I believe I answered this previously. Nylon if you can tolerate the cost.

3) I believe I answered this previously: Dominant.

Actually every violin is different. If you want a brighter sound, steel, with nickle or german silver, is the way to go. Want more complexity, gut. Hate tuning every 30-40 minutes, synthetic (perlon). Gut will give the most complex richer tone, but can make some violins too dark. Steel strings are the easiest to play. They sing quicker. They also can have the brightest sound. Helicore strings are tops for steel strings. Very bright, sing quickly, yet have nearly as much complexity as Dominants. The Dominants will be a touch darker than the Helicore, but will sing near as quickly, and do give a more complex tone. Dominants down fall is it's E string, which is as bright as the E with the Helicore. The best E string is the Vision Solo from Thomastic. Great sound, blends well with gut strings too.
The brightest, quickest strings I have played are Red Label. Followed by Black Diamond Fiddle strings. The darkest Synthetics I've played are the Eva Pirazzi's. I find the Pro-Arte strings from D'Addario are as good as the Dominants. You could also try the Tonica, Obligato strings too.
Gut strings will give the most complex tone. But they are the most expensive, need the most tuning, and wear out the fastest. Try Piastro's Passione, Eudoxa, or Oliv strings.
As a beginner, use steel. You have to break a few strings before you really know tuning. They last longer, play easier, stay in tune longer, and sound quite good on most violins. By the time you want a more expensive string for playing some thing for others to hear, you would have worn out the more expensive strings. SO wear out a few different steel strings first, then try the more expensive strings out. You really need your vibrato down well to appreciate the better tone from the more expensive strings anyways.
Rosin will be a bigger problem. You want enough grip for a good tone and no slippage, but also as low a build up on the strings as possible. Too much rosin and the rosin will build up on the strings and slip as bad as not enough rosin. Dust your violin and wipe the strings after every use. A low dust rosin is nice, IF it works. Play inside at moderate temps, and normal humidity levels, a light rosin should be your choice. BUT if it's cooler, or humid, then you may need a darker rosin. I use a very dark rosin on my fiddle's bow, and a very light rosin on my violin's bow. The fiddle gets played out side, where it's cooler and more humid.