From my perspective, the answer is, "Nearly any of the design software can be good for designing a logo for a website". Now, to some people, that response might sound like a way to sidestep the answer. Let me explain why I feel like that reply is a good one.
Factor 1 - The Cost of the SoftwareI do not know Mr. Panagiotopoulos personally, but many people looking for something "good" consider the monetary cost of the item when they begin looking at a product. Software can be very expensive or very cost effective. If this factor is weighted more heavily by the one posing the question, then open source software will likely be more appealing to him. If not, then one of the following bits of information may need to be considered.
Factor 2 - The Learning CurveAll software brings a learning curve for the new user. Often times this can be compounded when the individual is trying to learn multiple things at once. If the individual is an artist and is familiar techniques and principles in design, then all that is needed is for the person to discover how to carry out those tasks in the new software.
Occasionally though, very smart individuals may feel that the idea they have in their mind is relatively easy to create but find out that trying to learn design and software at the same time is not going to be very efficient. As a solution, the individual begins trying to find help using the software and realizes that in addition to having an intuitive user interface, having good documentation and support alleviates this challenge somewhat. These features are often times of a higher quality for the more expensive software bundles than they are for the lower cost, open source packages.
So it is easy to see then, that the first two factors can work against each other when trying to decide on design software. This is what brings us to the third aspect of choosing a design software package - the purpose of obtaining the software.
Factor 3 - The Software's PurposeThis aspect of the consideration really has multiple facets itself. The first of these is 'Will the image be used only for the web, or will there be print ready artwork created as well?' This is important because different types of images work better for each of these mediums of delivery. Additionally, there can be some hurdles if the incorrect software is used for specific graphics.
Another aspect of the software's purpose to keep in mind is the amount of work for which it will be used. The first project's requiring only a few features to complete does not necessarily mean that you do not need the additional features offered by the software. Having the ability to create other graphics and design elements can be very handy. What that means is that the software's purpose is often times the best place to begin when deciding on a design software package or bundle.
So, Nikos' question cannot really be answered the same way for everyone because circumstances will affect the decision. These are not the only factors to consider, but they are among the most important to think about.