I read this article on wikipedia which is about thirty three devatas (trayastrimsati koti). But there is no Ganesha in them.
I would like to ask in which category Ganesha Belong?
Yes , Shree Ganesh is true Deva or God and not only that he is said to be the the Brahman ,giving Consciousness to All. We can find his description In Ganapati Atharvashirsha (Ganapati Upanishad)
Here he is said to be the visible Brahman -:
त्वं प्रत्यक्षं ब्रह्मासि - । Tvam Pratyakssam Brahma-Asi
You are the visible Brahman (manifested as the Universe) (Therefore, O Ganapati, the Absolute Truth I have spoken will make the realized see this vast World as emanating from Sacchidananda)
त्वमेव सर्वं खल्विदं ब्रह्मासि - ।Tvam-Eva Sarvam Khalv[u]-Idam Brahma-Asi |
(O Ganapati) You indeed are All This (The Universe); You verily are the Brahman (giving Consciousness to All)
Here he is said to be INDRA ,AGNI ,SURYA ,CHANDRA ,WIND etc.
मिन्द्रस्त्वम स्त्वमग्निस्त्वं वायुस्त्वं सूर्यस्त्वं चन्द्रमास्त्वं ब्रह्म भूर्भुवस्सुवरोम् ॥६॥
Vaayus-Tvam Suuryas-Tvam Candramaas-Tvam Brahma Bhuur-Bhuvas-Suvar-Om
Meaning: You are Indra, You are Agni (God of Fire), You are ... Vayu (God of Wind), You are Surya (The Sun God), You are Chandrama (The Moon God), You are ... Brahman (Absolute Consciousness), You pervade the Bhur-Bhuvah-Suvar Lokas; You are the Om Itself (Parabrahman).
Here in the end we can find Rushi Gannaka calling him as a God.
सैषा गणेशविद्या । गणक ऋषिः । निचृद्गायत्रीच्छन्दः । गणपतिर्देवता । ॐ गं गणपतये नमः ॥९॥
Sai[a-E]ssaa Gannesha-Vidyaa | Gannaka Rssih | Nicrdgaayatriic-Chandah | Gannapatir-Devataa | Om Gam Gannapataye Namah
This is the Ganesha Vidya (A path leading to the Knowledge of the Self through the worship of Ganesha through His Mantra Swarupa), The Rishi who realized this Vidya is Ganaka Rishi, The Chhanda (Metre) is Nicrdgayatri, The Devata (God) worshipped is Ganapati, Om Gang Ganapataye Namah (My Reverential Salutations to Ganapati), I seek Your Blessings to practice this Vidya)
He is the son of Lord Shiva and Parvati. A interested story of his birth is also given in Vaman Purana. (Chapter 54 –Birth Of Ganesa). Although he is not mentioned in the list given by you in your answer. He is most popularly worshiped as a God worldwide.
in which category Ganesha Belong -: (Adi-Dev , Lord of Ganas,Para-Brahman)
Mahabharata accepts Lord Ganesha as a true Devata. After all it was Lord Ganesha who actually wrote the Itihasa (although this is not accepted by the Bhandarkar critical edition). I am also posting this additional passage that reinforces Lord Ganesha's claim to be a true Deva.
Narada on 5 deities
Narada said, ‘Thou art He who is the topic of the five foremost of scriptures (viz., those that appertain to the worship of Surya, of Sakti, of Ganesa, of Siva, and of Vishnu).
Mahabharata Santi Parva Section CCCXXXIX
Ganapati or Ganesha is a Vedic God.
Here is Vedic verse dedicated to him which is widely used as an Avahana Mantra for Lord Ganapati.:
ॐ गणानां त्वा गणपतिं हवामहे कविं कवीनामुपमश्रवस्तमम् । ज्येष्ठराजं ब्रह्मणाम् ब्रह्मणस्पत आ नः शृण्वन्नूतिभिःसीदसादनम् ॥ ॐ महागणाधिपतये नमः ॥
Om Gannaanaam Tvaa Ganna-Patim Hava-Amahe Kavim Kaviinaam-Upama-Shravas-Tamam | Jyessttha-Raajam Brahmannaam Brahmannas-Pata Aa Nah Shrnnvan-Nuutibhih-Siida-Saadanam || Om Mahaa-Ganna-Adhipataye Namah ||
1: Om, O Ganapati, To You Who are the Lord of the Ganas (Celestial Attendants or Followers), we Offer our Sacrificial Oblations, 2: You are the Wisdom of the Wise and the Uppermost in Glory, 3: You are the Eldest Lord (i.e. ever Unborn) and is of the Nature of Brahman (Absolute Consciousness); You are the Embodiment of the Sacred Pranava (Om), 4: Please come to us by Listening to our Prayers and be Present in the Seat of this Sacred Sacrificial Altar. 5: Om, our Prostrations to the Mahaganadhipati (the Great Lord of the Ganas).
Similar verse is in Yajurveda too:
Ganaanaam tvaa ganapatim havaamahé Priyaanaam tvaa Priyapatim havaamahé, Nidheenaam tvaa nidhipatim havaamahe. vaso mama. Aahamajaani garbhadhamaa tvamajaasi garbhadham. (Yajurveda: 23. 19)
Now,some people have confusion whether Brahmanaspati refered along with Ganapati in these verses is at all Lord Ganesha or Deva Guru Brihaspati.
Here is what i think:
These verses find place in the famous Vedic Suktam called the Ganapati Suktam .And these verses are widely used in all Vedic Pujas as avahana mantras for Ganesha.So,i can't believe that they will wrongly use mantras that are related to Brihaspati during Puja of Lord Ganapati.
Also from this page we find:
The word Ganapati accompanies the word Brahmanaspati in several mantras.The great Tantric and commentator in Veda ,Kapali Sastry declares that the deity Ganapati and Brahmanaspati are the same.
Ganapati is also one of the Pancha Devatas or the 5 (principle) Deities in Hinduism the other 4 being Shiva,Vishnu,Devi and Surya.So,he belongs to the category of Pancha Devatas.
In every Hindu ceremonies worshiping the Pancha Devatas is usually recommended.
Adityam GananAtham Cha Devim Rudram Cha Keshavam | PanchaDaivatyamityuktam Sarva Karmasu PujAyeth ||
Meaning-The Pancha Devas are -Surya,Ganesha,Devi,Shiva and Vishnu.In all ceremonies they should be worshiped.(Matsya Purana)