This app was mentioned in 1 comment, with an average of 3.00 upvotes
Here are some links:
This is the Psalter I used growing up (well actually we used red version until this one came out but they're very similar) there is also an app version: http://www.crownandcovenant.com/The_Book_of_Psalms_for_Worship_s/117.htm
Crown and Covenant has a free psalm you can download every month: https://www.crownandcovenant.com/Articles.asp?ID=123
Free app with 1650 split leaf psalter: https://play.google.com/store/apps/details?id=com.smouring.android.psalterapp&hl=en
As far as beginner psalms I would start with psalms you already know the tune to. Now that I'm in a hymn singing church the hymns that share psalm tunes have been the easiest to pick up and there is quite a bit of overlap. For example psalm 3 is to the tune of amazing grace.