Will people be able to see my web log? Also, how to make it so that my company doesn't know that I am surfing?
A lot of companies have web traffic/request monitoring tools installed so that they could monitor their employees' Internet/web usage. For example, I know of companies have surf control installed. So, the short answer is no. Try not to surf the Internet at work. However, if you do plan to do so, there are couple of ways you could do as follows.
1) Remove browsing history in Firefox or IE. Remember to always remove the web history in your local computer. However, even if you deleted the Internet browsing history with your browser, your web requests have been routed through your company's network. These requests are logged somewhere in your IT department.
2) Use a proxy server/site to surf the Internet. There are some proxy sites you could use to get around the surf control/web monitoring. Also, if you are a computer science guru, you can setup your own proxy server at home. However, using a proxy still has some drawbacks. If your company's IT admin is diligent enough, he would be able to track down the sites you visited, including the proxy site.
So, it is better not to surf the Internet at work, especially for your job hunting related surfing. But, using a proxy site/server is the best bet to get around that.
If you do plan to use a proxy site to surf the Internet, it is better to use a proxy service that allows https encryption. This way, web traffic to and from your desktop is encrypted. So your company couldn't decrypt the text you get/send.