Assuming that by Moksha you mean liberation from this material existence, not merging into he absolute (Brahman), following are the answers to your questions.
How many paths exist?
There exists four fundamental paths for attaining liberation. They are Karma, Jnana, Dhyana and Bhakti. But dhyana being a physical technique that can be used both in the Jnana marga and Bhakti maraga, the total different paths can be said to be three. Other paths like Yoga are subsets of these three. The Bhagavad Gita discusses about these different paths.
Can moksha be achieved through just one path/practice?
Yes, irrespective of any path you follow you will eventually achieve liberation. Just like many different roads lead to the same destination, the different paths lead to the same end objective of liberation. Paths like devotion are easy, but paths of Jnana, Dhyana are comparatively difficult. But you are not limited to only one path, you can follow all the there if you are eligible.
If not, what are the minimum combinations of practice, and in which order must they be practiced?
From the point of view of easiness one should start from Karma Yoga, then proceed to Bhakti and then to Jnana. Having the mind fixed only upon the Lord is the utmost objective, but its difficult too. So the Bhagavat Gita in the 12th chapter describes the order suitable for a person depending upon his ability:
Just ﬁx your mind upon Me, the Supreme Personality of Godhead, and engage all your intelligence in Me. Thus you will live in Me always, without a doubt. [BG - 12.8]
My dear Arjuna, O winner of wealth, if you cannot ﬁx your mind upon Me without deviation, then follow the regulative principles of bhakti-yoga. In this way develop a desire to attain Me. [BG - 12.9]
If you cannot practice the regulations of bhakti-yoga, then just try to work for Me, because by working for Me you will come to the perfect stage. [BG - 12.10]
If, however, you are unable to work in this consciousness of Me, then try to act giving up all results of your work and try to be self-situated. [BG - 12.11]
Is there weightage to these practices?
No, there is none. The thing is that, all these paths are circularly related. If you start from one and do it perfectly, you will automatically move to the other. Perfect devotion gives knowledge and perfect knowledge leads to the devotion of the lord. So there is no path small or big. It only depends upon the eligibility of the practitioner. Irrespective of whatever path you follow, when done perfectly it will award you knowledge. And perfect knowledge can lead you to the jivanmukta state, that is liberated while living. It is because knowledge destroys every kind of action(BG - 4.37) and it is only action that acts as the seed of repeated birth here.
However, one thing to remember is that, because these are different paths, the experience you'll have will be different. That is, even though you'll achieve liberation from this material existence, where you will go and your experiences will be different. See this answer for different objectives of different types of practitioners.
You have actually asked very important questions. The complete answer to these cannot be given briefly. Discussing these in brief with scriptural quotes took around thirty pages on my book. So I have answered the gist here without quoting much scriptural verses. If scriptural references are required, then I can add them later when I get time.