In regards to establishing an altar in your home I can only tell you what I have done and what I do. We are each individuals and will do things in our own ways. Also even as different individuals we are all developing on our own timelines, and so even a single individual will do different things in different ways at different times.
The first thing, in my opinion, was to establish who my “Ishtha-Deva” is. That term means “dearmost lord.” For as long as I have had altars my ishtha deva has always been the Goddess of Devotion, Srimati Radharani with her dear object of devotion, the intimate Sri Krishna, playing a flute. So I have almost always had these two as the central focal point of my altars.
Then it is simply a question of putting the right supporting personalities and elements in place. For example, Radha and Krishna’s specific MOOD is expressed in a cozy, forest-type setting – not in big cold opulence, etc. So you know, I like to have cozy warm opulence like cloth with rich colors and nice patterns, planets, greenery, you know, some peacock feathers, that sort of thing decorating the altar to create the right supportive mood in which my istha-deva can more fully manifest to my emotional and mental and physical being when I am in contact with my altar.
Then there is the question of supporting gods / angels / beings / gurus / teachers etc. Personalities who help me make contact and connection to my Ishtha-deva. So for example I like to have Sri Caitanya Mahaprabhu and his brother Nityananda Rama on my altars, usually in a pose of dancing while singing the names of Radha and Krishna. I find this personally helps me connect. I also like to have pictures of various persons who have been very important in helping me connect to my ishtha-deva. For example I like to have pictures of the six goswami’s of Vrindaban (the immediate disciples of Sri Caitanya), and some of the gurus in my line who particularly and specifically have helped me personally.
So the whole thing rests on determining who your Ishtha Deva is. The more detail you know this in, the more specifically and powerfully you will start to arrange your altar. In the early stages of spiritual development we have to do a lot of work to figure this out – and we should remain flexible, as it is sure to develop and clarify as we progress in our meditations and spiritual practices.
Once you have a basic idea of who your Ishtha Deva probably is, you then face the question of how to represent that person on the altar. The simplest way is to find a picture of your Ishtha Deva that is very moving to you, spontaneously, and use that. You can perhaps very nicely frame the picture, etc.
Later on, after you have progressed and are more confident in your Ishtha Deva you may wish to seek a three-dimensional representation to make your altar more powerful and engaging to your mind and senses and activities. When that time comes your Ishtha Deva himself/herself will help you find the appropriate “statue” or “deity.”
This is just based on my personal experience. I hope it helps you.