I had a Mail2web account for 9 years but left after they completely failed to resolve a major problem with their billing system then started threatening me for not paying! There is a lot of arrogance in their customer service team that seems to focus efforts on winning petty arguments with customers instead of resolving problems. I moved to Microsoft hosting which it turns out is cheaper I also have more control and, significantly, much more up-to-date applications. I realise now that the Mail2Web Outlook web access in particular is completely outdated. And when using desktop apps searching emails on the server is much quicker and more reliable. Interestingly I also receive far less junk mail since moving away from Mail2Web despite my email address being exactly the same.
So in conclusion Mail2Web is overpriced, out of date and poorly supported. I cannot think of anything worth recommending.