First of all, I am not a Vedajna. In fact no one in this world except God Himself is a true Vedajna even if many claim or act as if they are:
In the entire world no one but Me actually understands the confidential purpose of Vedic knowledge. Thus people do not know what the Vedas are actually prescribing in the ritualistic injunctions of karma-kāṇḍa, or what object is actually being indicated in the formulas of worship found in the upāsanā-kāṇḍa, or that which is elaborately discussed through various hypotheses in the jñāna-kāṇḍa section of the Vedas. [SB - 11.21.42]
But by the grace of God and my gurus I could know the essence of the scriptures and know enough to answer your question.
There are only three paths (yogas) of karma, bhakti and jnana for the spiritual advancement of a person:
yogās trayo mayā proktā nṝṇāṁ śreyo-vidhitsayā
jñānaṁ karma ca bhaktiś ca nopāyo ’nyo ’sti kutracit [SB - 11.20.6]
The Supreme Personality of Godhead said: My dear Uddhava, because I desire that human beings may achieve perfection, I have presented three paths of advancement — the path of knowledge, the path of work and the path of devotion. Besides these three there is absolutely no other means of elevation.
So by following anyone as per one's ability one can eventually come to the realization of his identity with Brahman. The thing is, jiva has similarities with Brahman and essentially both are one. But due to ignorance jiva identifies himself with the body and all other material attributes without realizing his true self. This ignorance is maya and whenever this maya in the form of avidya is is crossed the realization occurs.
So irrespective of the path followed if one acquires the right knowledge he realizes aham brahmasmi. This is where various philosophy and methods come into action.
To destroy ignorance some suggest acquiring knowledge through self inquiry and repeated contemplation on the truth that the self is Brahman - this is the path of Jnana. So the Veda says this atma alone should be heard, seen and thought upon:
ātmā vā are draṣṭavyaḥ śrotavyo mantavyo nididhyāsitavyo [Brh. Up - 2.4.5]
-Verily it is the Self alone that should be seen, heard, thought and pondered over.
Some suggest ceasing the mental activity and fixing it upon God alone - this is the path of yoga/dhyana yoga constituting eight limbs of yama, niyama, etc. Even by practicing this one gains the knowledge of oneness of God:
sarvabhūtasthamātmānaṃ sarvabhūtāni cātmani
īkṣate yogayuktātmā sarvatra samadarśanaḥ [BG - 6.29]
The yogi sees his own self in every being and sees every being in his own self. He sees everywhere the same.
Some suggest practicing devotion of God and through his grace the devotee automatically gains knowledge without any inquiry, etc:
teṣāṃ satatayuktānāṃ bhajatāṃ prītipūrvakam
dadāmi buddhiyogaṃ taṃ yena māmupayānti te [BG - 10.10]
To those who constantly practice devotion to Me with love, I give them the knowledge by which they come to Me
But because the nature and interest of people are different, different kinds of philosophies (samkhya, mimansa, yoga, vaishesika, etc.) and their corresponding paths have come into existence including atheistic ones:
Thus, due to the great variety of desires and natures among human beings, there are many different theistic philosophies of life, which are handed down through tradition, custom and disciplic succession. There are other teachers who directly support atheistic viewpoints. [SB - 11.14.8]
And about these plethora of philosophies and practices that the Shiva Samhita talks about in those verses. It is the nature of all scriptures of a particular system to shun other systems and paths so that the seeker may not get bewildered by trying to follow different paths of opposite views. It doesn't mean other two paths are wrong or less important. But the warning is valid because apart from the accepted philosophy and systems there are also systems like Charvak which are faulty and wrong.
Just like Shiva Samhita being a yoga text encourages Yoga alone as the right path, Shrimad Bhagavatam being a Bhakti text encourages Bhakti alone as the surest path. Uddhav asks similar questions like you regarding what is the presecribed path of the Vedas. And Shri Krishna in response clears his doubts answering his questions one by one:
Śrī Uddhava said: My dear Kṛṣṇa, the learned sages who explain Vedic literature recommend various processes for perfecting one’s life. Considering these varieties of viewpoint, my Lord, please tell me whether all these processes are equally important, or whether one of them is supreme. [SB - 11.14.1]
The Supreme Personality of Godhead said: By the influence of time, the transcendental sound of Vedic knowledge was lost at the time of annihilation. Therefore, when the subsequent creation took place, I spoke the Vedic knowledge to Brahmā because I Myself am the religious principles enunciated in the Vedas. [SB - 11.14.3]
O best among men, the intelligence of human beings is bewildered by My illusory potency, and thus, according to their own activities and whims, they speak in innumerable ways about what is actually good for people.[SB - 11.14.9]
Some say that people will be happy by performing pious religious activities. Others say that happiness is attained through fame, sense gratification, truthfulness, self-control, peace, self-interest, political influence, opulence, renunciation, consumption, sacrifice, penance, charity, vows, regulated duties or strict disciplinary regulation. Each process has its proponents. [SB - 11.14.10 ]
All the persons I have just mentioned obtain temporary fruits from their material work. Indeed, the meager and miserable situations they achieve bring future unhappiness and are based on ignorance. Even while enjoying the fruits of their work, such persons are filled with lamentation. [SB - 11.14.11]
O learned Uddhava, those who fix their consciousness on Me, giving up all material desires, share with Me a happiness that cannot possibly be experienced by those engaged in sense gratification. [SB - 11.14.12]
One who does not desire anything within this world, who has achieved peace by controlling his senses, whose consciousness is equal in all conditions and whose mind is completely satisfied in Me finds only happiness wherever he goes. [SB - 11.14.13]
(Please read that complete conversation and also this one and your doubts will be cleared)
Philosophy is nothing but a set of ideas and theories that gives an idea about the object and ways of life. It is a theory that puts the questioning mind into rest. But a philosophy can also have a practical aspect to it without following which dry philosophy is of no use. For example, yoga school of thought enjoins the practice of the eight limbs of yoga. The system of Bhakti enjoins practice of chanting, singing, etc. Vedanta school of thought enjoins contemplation upon Brahman and so on. So most philosophies have practical aspects also which should be followed.
...and what about discipline? Well, discipline is the minimum thing that everyone should follow irrespective of whether one is spiritual or not. In the path of jnana it is mandatory to live a disciplined life. In the path of Bhakti it is mandatory to remember God always whether you are disciplined or not. But at the end of the day, discipline is the foremost requirement for any spiritual practice. A disciplined life is a spiritual life, otherwise it's not.
Is there any mentioning/praising of yoga-marga/yogic path in vedas?
Yes, there are many Upanishads like Nadabindu, Tejobindu, Yogasikha, etc. that are classified as Yoga Upanishads. In them the path of yoga has been mentioned and praised.