I don't think it's against Amazon's terms of agreement - Amazon is pretty reasonable. You might, however, also want to include a few text links related to your site's topic.
And if you have time to do direct links to individual books or other products related to the site, along with information for your visitors on those links (even a few words), you will probably get a good response. Links to new books related to your topic might be especially popular. It's a service to your visitors. I prefer text links and find they work well.
Better check amazon's tos. I don't think you're supposed to directly ask people to give you a commission by buying through your links instead of going directly to amazon. There may be some leeway in how you word it and/or present it, but check the agreement.
Yes, check the agreement definitely, but I don't think Amazon is going to have a problem with this. I have a note on my site explaining that I get a commission from sales. When I added it with a link to Amazon's homepage, sales through my site went up.
It isn't like Adsense where you're getting paid for clicks. You're only paid for sales, and Amazon wants any customers you can send because that means they're not going to other sites to shop. So you're not harming Amazon in any way by giving customers a reason to go to Amazon (ie to support your site).
However, as I said, you might find links to certain products or sections more profitable. Amazon sells tons of stuff and many people don't even know all the different things they sell. Giving your visitors a little info relevant to their interests can't hurt and usually helps. (I mentioned text links because I find them to be better than image links.)