I would strongly recommend against using Google’s Chrome. No way no how!

Google essentially wants you to walk with a homing beacon and that they can follow your every move, listen to everything you say, all so that they can show you more precise advertising and gain more money. Now, in real life people don’t agree to this, but somehow on the net they do. What is their trick? Well, one of them, is that they “combine” the search bar with the address bar. So, every time you type in an address you want to go to, it goes to them! Not simply what you search for but every address you type in. They have other tricks, like that you can search Amazon from the address bar – again, they get all the information. And many more like this.
Now, some of these things you can change from the default, but most won’t do it – and they care about the masses – but also, it is not at all clear that enough, or that you don’t just give this information to a different company than google for advertisement.

Already some agencies started recommending not using it, and some parts of their user agreement they changed after outcries that it was blatantly illegal. But the major part stays put – they follow everything you do.
Now there are hilarious articles which write how what they are doing and the information they gather is to “provide you with better search results”!! It is not meant as a tool to provide you better search results but as a tool to gather as much information about you so they know what to sell you.
Personally, I don’t understand why people are so willing to give up any shred of privacy without any reason whatsoever, while from the government or others they do think they should have privacy. There are other browsers, other email accounts. Perhaps search engines there really isn’t anything else worthwhile, so we use it. Also, it is not that other companies are necessarily better, only you don’t want one company to rule all your information. It is much safer when your information is scattered and is not held by one entity which knows every tiny detail about you.

As for recommendation: Mozilla’s Firefox as browser and Thunderbird as email clients are good possibilities. Mozilla is quite a nice community, and it is nice to support them. They are trying now to figure out the delicate balance of being a free user-developed browser, with wanting to supply their programmers with money to be able to compete with the big boys who are trying to rule the market (Microsoft, Apple, and Google).

For a good free email account, I would probably stay clear of gmail for some of the same reasons as above, as it is some more details google knows about you. Basically they are all somewhat the same. There are also: mail.yahoo.com or Microsoft's hotmail. I would probably today go with yahoo as the least offensive.

The best browser right now is probably Firefox. It has many addons if you want to use them, or you can use it simply without anything. It is at the moment the biggest competitor to Microsoft’s Internet Explorer.
Opera has some nice features, some nicer than Firefox, but mostly I just find it really annoying to use. Perhaps one can dig deep into its preferences and correct some of them, but I doubt it, and anyway, it’s too much work.
Safari I don’t personally like either. It is quite difficult to erase your private data and takes many steps, while in firefox and opera it is very easy. It is a barebones browser without many possibilities, but might appeal to the mac fans.
Internet explorer is in general, security wise, a very bad decision to use. I don’t really know how good it is to use as I don’t use it much. It is still the most widely used browser as it comes installed with your operating system, and the default is always the most widely used.

There is also Chrome, but I agree with Hugh and wouldn’t go near it with 10 foot pole. It is probably technically  good though as they have good programmers, and they spied on Firefox the last couple of years in the guise of helping them and letting their programs work part time there “for free.”    

Anyway, you can’t really go wrong with choosing Firefox, but you might want to take a look at others and see if you personally like their interface more.

As for email clients, Mozilla’s Thunderbird is extremely good and easy to use. There are others but I don’t know much about them. (Microsoft Outlook, or Outlook Express I would recommend against from security reasons). Regarding free email accounts, I have nothing to add to what Hugh said.  

I’d also add to Hugh’s point about privacy that I can see people giving up their privacy for good reasons. To carry a mic around you all the time if it can help people, or even reality TV shows where people want to show themselves. Most of google stuff on the other hand has very little benefit to society or you, though they do have some good products like their amazing search engine, and google maps. You give up some privacy when you use the search engine, but ok, you get a lot in return; there is no real reason to use gmail though, unless their nice interface is more important to you than your privacy, as that is all you get.

The problem with google is that they are simply too invasive on too many fronts that all together it gets to be very dangerous for society, even if in the micro scale, or one service at a time, it is ok.