The original circuit simulation software, called the Simulation Program ... not all of which are as open or free as we might like. Qucs is a GPL circuit simulator. And if you want the GUI option ...

Need to find out what is application of that circuit and based on that different types analysis needs to carried like Transient analysis, AC/DC analysis, stability analysis and also the Noise ...

The first factor to consider is the type of circuit you are working on. Is it a linear or a nonlinear circuit? A DC or an AC circuit? A digital or an analog circuit? A passive or an active circuit?