Actually, if you were present when your archen hatched, then it very likely imprinted on you, and thus, it may be better off with you than with a professional—if you can give it adequate care, anyway.
That having been said, as a bird pokémon (essentially, anyway), it needs many of the same things birds would: safe housing (where it can perch at night or where it can eliminate its wastes), clean drinking water, enough food to feed it twice daily, a means of keeping it entertained and enriched, and an abundance of affection. Just like many other birds, archen will vocalize to locate and reassure itself of the presence of its flock—you, in other words. So be prepared for a rather loud or talkative pokémon.
Also, despite possessing fangs, archen are actually herbivorous, and they prefer whole fruit to seeds. However, if feeding your archen kibble, keep in mind that archen-specific kibble does not exist, but archen can and will eat either generic poké-kibble or kibble designed for certain bird pokémon (namely chatot, swablu, pidove, or ducklett). If going with any of these choices, you may need to supplement your archen’s diet with vitamins. Your Nurse Joy will be able to tell you if that’s the case.
Additionally, as archen are rock-types, the water should only be used for drinking. Never bathe your archen if you can help it. Rather, provide it with a sand bath separate from its cage (preferably outdoors, as it will fling sand everywhere in the process of cleaning itself). While it self-grooms afterwards, a great bonding method is to help it to preen by sitting it beside you and brushing its feathers with a standard pokémon brush.
In terms of exercise and behavior, archen are very easy to train, as they’re more eager than a number of other pokémon to battle. As ancient pokémon, they are also highly curious and prone to wandering off if left unattended. In other words, while archen and archeops are typically eager to listen to you on the battlefield (not to mention easy subjects to train when it comes to teaching moves), they can be quite a handful off the battlefield. When going out, be sure to keep your archen or archeops secure in their poké balls, and when at home, keep an eye on it and keep it away from both wild pokémon and those of your neighbors.
Generally speaking, archen and archeops are fascinating pokémon that I admit are far less understood than I’m implying above. For this reason, you have a wonderful opportunity to befriend and study one of the rarest pokémon in existence, and for that, I admit I’m a little envious. Nonetheless, I wish you the best of luck, @jun-mon, both on caring for your new archen and learning more about its species through your experiences.