Hi, you can use MEGA 5 or 6. Its user interface is very easy and provides very good functionalities. You can also give a try for clc bio or ncbi tools.
Many of the commonly used programs (such as RAxML for maximum likelihood inference, and Mr.Bayes or PhyloBayes for Bayesian) are used through a command-line interface, and so if you are not familiar with working in this sort of environment than there will be somewhat of a learning curve. However, you can use many popular command-line only software through the CIPRES web portal (https://www.phylo.org/) which will run the software on one of the XSEDE machines.
I've attached a paper which I think might be beneficial for you. Hope it helps.
I also recommend MEGA and Seaview, nevertheless the real thing in which you must concentrate is the method of reconstruction, such as maximum likelihood, neighborjoining, parsimony, Bayesian, etc. The election of the method is based on the nature of the sequences, and even on what kind of question you want to answer with the phylogenetic analysis.
Yes in a first step the Molecular Evolutionary Genetics Analysis (MEGA) software is a good choice that enables users lacking experience to easily explore their data and to reconstruct phylogenetic trees using different criteria (distances, Maximum likelihood, Maximum parsimony).
The Yang and Rannala paper is superb. If you have a Mac, i'd recommend using Seaview as running MEGA on a Mac is a bit of trouble. On the other hand if you have a PC then MEGA is great.
By the way I agree with Alberto. There is no simple and easy way to do phylogenetics despite the fact that sequences are often run through these programs and results are generated with default parameters which is never a good idea, particularly for Bayesian analysis. All methods depend on a good alignment and determination of the proper model of sequence evolution whether you use distance, Maximum Likelihood or Bayesian analysis.
So get to know an experienced phylogenticist and check you methods and results before submitting for publication. And know the biology well enough to know what question you are asking.