How many distinct independent paths/practices/methods are there to achieve Moksha?
Can moksha be achieved through just one path/practice?
If not, what are the minimum combinations of practice, and in which order must they be practiced?
Is there weightage to these practices, for example, a particular practice is valued 10 times another one?
Assuming that by Moksha you mean liberation from this material existence, not merging into he absolute (Brahman), following are the answers to your questions.
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.
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.
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]
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.
Moksha is the goal of only Advaita Vedantins. There are broadly 2 distinct paths. I am posting below a conversation from Mahabharata, Adi Parva, Section XCII which discusses these distinct paths:
Ashtaka asked, 'Who amongst these, O king, both exerting constantly like the Sun and the Moon, first attaineth to communion with Brahma, the ascetic or the man of knowledge?'
Yayati answered, 'The wise, with the help of the Vedas and of Knowledge, having ascertained the visible universe to be illusory, instantly realises the Supreme Spirit as the sole existent independent essence. While they that devote themselves to Yoga meditation take time to acquire the same knowledge, for it is by practice alone that these latter divest themselves of the consciousness of quality. Hence the wise attain to salvation first. Then again if the person devoted to Yoga find not sufficient time in one life to attain success, being led astray by the attraction of the world, in his next life he is benefitted by the progress already achieved, for he devoteth himself regretfully to the pursuit of success. But the man of knowledge ever beholdeth the indesctructible unity, and, is, therefore, though steeped in wordly enjoyments, never affected by them at heart. Therefore, there is nothing to impede his salvation. He, however, who faileth to attain to knowledge, should yet devote himself to piety as dependent on action. But he that devoteth himself to such piety, moved thereto by desire of salvation, can never achieve success. His sacrifices bear no fruit and partake of the nature of cruelty. Piety which is dependent on action that proceedeth not from the desire of fruit, is, in the case of such men Yoga itself.'
