There are several questions being asked here.
1) What is the point of disciples being poor? I do not believe that disciples are required to be poor. Rather I believe that they should have open eyes of how their blessings can be shared or passed along to others. God wants us to use what He gives us to show love to and care for others.
2) What kinds of poverty are there? People can be poor in spirit, as referenced in the verse you mentioned. This means they are humble and do not set themselves up boastfully as being grand or one of high importance. People can be monetarily poor, having little or no monies or possessions. We can also be poor in health with illness being our poverty. Poverty can also be social, with sufferers being or feeling like an outcast.
We are called to share our blessings with those suffering from all types of poverty: to give to those without, to heal those in need, and love everyone, including the least of these.