Namaste,
I’m considering to buy a Vishnu murti. I’d like to know about some traditions that worship Vishnu.
There are many, but just look at the link Achintya-Ash has posted.
Who is considered the supreme god according to these traditions, Vishnu or Krishna?
While this is a stark difference between the sampradayas of the North and the South, this is not a topic of severe debate among them. In either way, they are both Lord Sri Hari, Vaikuntha-pati, and the Purusha praised in the Vedas, so there is really no difference between them. It's not like we are comparing Sriman Narayana and Lord Shiva.
Which mantras are suitable for Vishnu?
Many Vishnu mantras require initiation, so there are some mantras that you should stay away from (The Namo Narayana Mantra -add a pranava before the Namo)
Do I need to worship Lakshmi with him?
In Sri Vaishnavism, this is a must.
The reason for this is that Bhagavan is angry at us because he is seeing all of our sins. He has given us his Shastra with the do's (the punyas) and the don'ts (the papams), so we cannot blame him for being angry at us (although some Hindus here like to say that there are no "do's or don'ts in Hinduism).
This is why we resort to Mother Lakshmi first. She is an arbitrator. After we have confessed our sins to her and have promised to not repeat them, she removes our sins and then talks to Bhagavan to award us Moksham. This is why Sri Vaishnavas surrender to Mother Lakshmi first and then to Sriman Narayana (our pUrvachAryas have said that the holy name of Vishnu must always be preceded with the holier name of Lakshmi).
Regards