I am desirous to undergo upanayana ceremony in one of the sanathana dharma sanstha.. So I don't know at all that any body underwent Upanayan in our caste. Before I undergo such ceremony, do I need any regret god or prayaschitta? If not, will there be any harm to my family?
Yes you need to do penance before Upnayana.
He, whose father and grandfather have not been initiated, (and his two ancestors) are called 'slayers of the Brahman.'
If they wish it (they may perform the following) expiation;
In the same manner as for the first neglect (of the initiation, a penance of) two months (was) prescribed, so (they shall do penance for) one year. 35
Afterwards they may be initiated, and then they must bathe (daily).
For as many years as there are uninitiated persons, reckoning (one year) for each ancestor (and the person to be initiated himself),
(They should bathe daily reciting) the seven Pâvamânîs, beginning with 'If near or far,' the Yagushpavitra, ('May the waters, the mothers purify us,' &c.) the Sâmapavitra, ('With what help assists,' &c.), and the Âṅgirasapavitra ('A swan, dwelling in purity'),
Or also reciting the Vyâhritis (om, bhûh, bhuvah, suvah).
After that (such a person) may be taught (the Veda).
Harm to family, No In fact vedic karma(Karma prescribed for everybody in vedas) is always purifying and Bhadra(good/auspicious), you don't need to worry about affecting family members.
Acts of sacrifice, charity and penance are not to be given up; they must be performed. Indeed, sacrifice, charity and penance purify even the great souls. BG 18.05
So purify yourself and get ready to attain supreme position in lotus feet of Lord.
If the penance is not done your karma will be affected.
If you don't have time, you have to resort to other means
Since there is limited time for Initiation of Different Dwija Varnas.
There is no dereliction (of duty, if the initiation takes place), in the case of a Brâhmana before the completion of the sixteenth year, in the case of a Kshatriya before the completion of the twenty-second year, in the case of a Vaisya before the completion of the twenty-fourth year. (Let him be initiated at such an age) that he may be able to perform the duties, which we shall declare below.
The sin is equated to Brahmahatya so you can also resort to the penance for Brahmahatya.
Or you can consult any scholar or acharya, they can help you with initiation by quickly performing Penances.
You can consider rama nama japa, it equals 1000 Vishnu Sahasranama.
First of all only the three dvija(Brahmin,Kshatriya,Vaisya) castes have the Upanayana samskara.Now, even if i assume that you are born in a family belonging to any of the 3 castes its clear that your family is not following the traditions since many generations.
In those cases the the persons belonging to that family are considered as having lost their caste and it(the caste) can not be recovered even by Samskaras.
From the book Hindu Dharma:
If the Gayatri has not been chanted for three generations in the family of a Brahmin, its members lose caste (they cease to be Brahmins). The quarter where such Brahmins live cannot be called an "agrahara". It is perhaps not yet three generations since Brahmins gave up the Gayatri. So they still may be called Brahmins.
In the same way if the Brahmin family has not performed sacrifices for three generations its members will be called "Durbrahmanas", degenerate Brahmins. Even though degenerate the label "Brahmin" sticks to them. There are prayascittas (expiatory rites) by means of which the corrupted Brahmins will be remade true Brahmins. But there is no such hope for a Brahmin in whose family Gayatri has not been chanted for three generations. A member of such a family ceases altogether to be a Brahmin and cannot be made one again. He is just a "Brahmana- bandhu", a kin or a friend of Brahmins. The same rule applies to Ksatriyas and Vaisyas with regard to the Gayatri mantra; they become "ksatriya-bandhus" and "Vaisya-bandhus" respectively.
About "Hindu Dharma" :
"Hindu Dharma" is a book which contains English translation of certain invaluable and engrossing speeches of Sri Sri Sri Chandrasekharendra Saraswathi MahaSwamiji (at various times during the years 1907 to 1994).
So,IMO upanayana is not recommended for you.