Instead of creating your own browser as other people have suggested, you can use an existing app: Kiosk Browser HC, and for a little price (after all you won't pay that so that shouldn't be a worry) there's an improved version: Kiosk Browser SE.

According to the version of the OS and if you can root the tablets or not, that might be all that you need, but if there's some other requirement then check SureLock Kiosk Lockdown

I don't know which browser you're using, but with Firefox it automatically shows a status bar with the destination of the link as soon as I hover it.

Sorry, clicked wrong while moderating the post.

And what happens with new sites (specially mobile versions) that use webkit only css features instead of using a standard approach?

Why can't they add the vendor prefix for the other browsers as well?

Although not stated as "best viewed with..." they are hurting the forward development of the web by sticking to just one vendor and we are going to suffer the same IE6 problems that we hate so much, but now it's webkit the culprit

Go to the Firefox button, Options and check Menu bar. For the status bar, install the status-4-ever extension

I also thought at the beginning that not having the status bar would mean a lack of UI that I will miss very much, but the fact is that I only really need it while I'm hovering a link and in those cases it automatically pops up, so I'm perfectly happy of not having those pixels wasted.

If you look at other comments, people still complain that there's still too much UI in Firefox, and all the browsers have been focused on cleaning up the UI. There's no reason to keep the same metaphors and UI elements than 20 years ago, browsing the internet should be easy and focused on that: browsing the web, not looking at the UI of the browser. I don't mean that the current trends are perfect, but rejecting any changes doesn't help us to move forward; of course sticking to a very old version and then jumping to the latest one will mean lots of changes but staying updated helps to take the changes little by little.

An example of something that I don't like/understand about the current Firefox is that Panorama thing. It could be useful if it could handle all the Firefox windows and tabs, but instead it just allows to group the tabs inside a window and hide the rest so I did test it a little and then forgot about it. The problem might be that someday they fix it and start behaving really well but I will miss it because they introduced it in a broken state and so I no longer have any interest about it

Google is already serving webkit-only css in the mobile versions, so when people try Firefox mobile those sites don't work as nicely as the default browser in Android, although Firefox is perfectly capable of handling them if they were coded properly.

Don't overestimate Safari.
If we have crossbrowser sites today is thanks to Mozilla, Apple is happy to copy anything from IE instead of trying to push the developers to use the W3C standards and if Mozilla didn't make a stand on many fronts (like ActiveX or recently H264), the web would be quite different.

Google is already quite good at pushing their browser as a side-install along with many unrelated products even of third party companies and you'll be lucky if you can get through the day without visiting some sites (as long as you're not using AdBlock Plus) and being offered to speed at greater speed thanks to Chrome.

And it will inject another plugin into Firefox just in case you did found out how to remove the previous one.

But do you know why it won't be possible to use those new grid features introduced in IE10 for a long time?

You won't be able to use them because IE10 will be available only in newer versions of Windows, (I don't know if even Vista is supported), so taking into account the people that just stick with the browser that came preinstalled and the long time until all those older versions of Windows disappear, it will take several years until the number of users with those versions is low enough.

The rest of the people with Firefox, Chrome, Opera will update at a more steady pace, so when the developers add those features you'll know that in a few months you could start using it if you're able to ignore old IE versions.