Yes, I agree that those are socialist ideas. And I agree that there's good and bad in every system, and it is entirely possible to incorporate elements of every system. But as far as capitalism goes, I think it's the one system that gives an individual the most control over his or her own success or failure. On any other system, an individual's success or failure is dependent on how competently the people in power implemented it--i.e. factors that are beyond the individual's control.
For example, in my country, medicare and social security in particular are going bankrupt, and a lot of people entire their retirement years worried that their social security money will be gone or they won't get enough to live on. As for welfare, I think that it's a great thing to have when we have the money for it, but at the moment we don't and we're constantly having to borrow money in order to fund it. I'm sure this isn't the case in other countries, but still, the quality of healthcare/food benefits/retirement money people get is dependent on factors beyond the control of the individuals receiving them.
I don't believe that the socialistic ideal is wrong. The very idea of everyone having equal possibilities and equal rights seems really admirable to me, but the problem lies in the execution of socialistic ideals in the real world. People are greedy, people want to get as much as they can - be it power, money, or even prestige, and this makes a socialist world a terrible thing in practice. If you get the same benefits, the same money, and the same prestige from every possible job, who will choose tough jobs? Nobody! Therefore socialist states have had to force people into certain positions and force them to work. An ideal world to me would be socialistic. Definitely. But our world is far from ideal, and a true socialist state is not a viable option in our society.
On the other hand, I do believe that a true capitalist ideal is wrong. A system based purely on profits - feathering one's own nest - purely benefits the richest. I do not believe that a system that benefits only the strongest will make life better for the average person.
I don't think that we should devote ourselves to one particular belief, but rather try to find the golden mean. The system that we have here in Denmark - a welfare state solidly grounded in one of the highest tax percentages in the world - is, in my opinion, somewhere near that golden mean. A social security system that grants everybody the right to free healthcare. A system where even if you have lost your job, the state gives you enough money to keep living in your house and get food on the table. And every persons right to free education. Everybody should have the same possibilities, so that even the child of the poorest family will have the possibility to attend the best university in the country!
Our system is not a system where everybody is equal, but rather one where everybody has equal possibilities. As long as one does their best it doesn't make a difference whether one's parents were poor or rich. Everybody is able to shape their own future through an education system that is free, and gives you enough money while studying for one to focus on their study and end up in a better position.