No bowser is completely safe. It also depends on how you define safe. Safe from what? Intrusions? Infections? Ads? Chrome is reputed to be the safest browser but Google is infamous for being nosy, collecting data, such as browsing habits, from people. One result of that data is what you have observed: targeted, annoying ads. I personally don't trust Google any further than I can spit upwind in a stiff breeze.
FireFox has been extremely popular but that popularity has been waning lately because of the frequent (and, thus, annoying) updates it has been doing lately.
I personally feel IE has been getting a bad rap because of it's less than stellar history. IE6 was a piece of work and IE7 wasn't much better. IE 8 was pretty decent and IE9 is even better (I use IE9 and like it; I've tried FireFox and just didn't like the way it was set up but that is just personal taste). IE10 has been getting good reports on the beta version. I'm going to wait, however, until the final version has been out for a while to see what the reviews are since “final” versions are often different than beta versions (and are often buggier than a flophouse bed).
Even more important than which browser you use for safety is how you use it. Avoiding dodgy websites (porn sites are notorious for being malware ridden), good passwords, and using a good AV and other malware programs contribute more to browser safety than the browsers themselves.
There are many AntiVirus programs (AVs) one can choose from. The paid suites contain everything you would ever need but usually contain too much which can slow your computer down. They also have to be renewed every year which can get expensive. However, they are they are the easiest and most convenient to use since they do everything for you. There many free alternatives, most of which are much lighter than the paid suites but require you to manually run scans and, often, download updates.
Microsoft Security Essentials (MSE) is what is most frequently recommended on the various computer geek sites. I’ve had problems with it not updating because of the way it is designed to operate is dependent on the computer being on at a specific time of day. I also found it was letting some tracking cookies in (they usually aren’t dangerous but some can be). I personally prefer AVAST! Free. It automatically updates several times a day, more often than MSE, and does so no matter when you are on the computer. I’ve found it better for blocking malware than MSE. If one doesn’t use too many of its extra bells and whistles, it doesn’t slow one’s computer down any.
The free version of MalwareBytes AntiMalware (MBAM) is a good program to have in your antimalware arsenal to catch viruses, trojans, etc. that slip past your computer. Super AntiSpyware (SAS) is another good one for catching spyware, such as tracking cookies.
All of the above programs will play well with each other as long as you never have more than AV installed at a time.
Web of Trust (WOT) is great for alerting you to known and potentially dangerous websites. AVAST! Free also has a similar feature but, since it depends on reports from users and hasn’t been around as long as WOT, it’s not quite as good. It is getting better. I use both and it doesn’t seem to slow my computer any.
Ads are more of an annoyance than a real danger as long as you don’t click on them or roll the mouse pointer over them. I use the paid version of Simple AdBlock (it’s a lifetime license) to get rid of the vast majority of ads. I resisted doing so for years because ads are what pay for websites but so many of them were becoming obnoxious (such as loud audio and/or annoying, distracting animations) or intrusive (popups that obstructed viewing the site’s content) so I finally broke down and installed the ad blocker.
Firewalls are an important line of defense against malware. Win7’s fire wall is excellent and is the one I recommend for most people since it works in the background and doesn’t require any computer chops to use it. I prefer Zone Alarm’s free firewall because I can easily control which internet transmissions are to be permitted in or out. Many people don’t like Zone Alarm because of the frequent popups when it is first installed but I’ve found if one takes time to read the popup before clicking on it to get rid of it, the program will quickly train itself and the popups will become rare.