Unless your website is very low traffic, the Amazon micro instance will not hold up very well and you find that stepping up to the medium or large instance (= more money) may be required.
That said, there are too many ways to list here to check that any Apache server is secure. this Google search will get you started.
http://goo.gl/SM9sB
Amazon S3 with reduced redundancy will cost about $45.00 per month plus the cost of the initial data transfer in. EC2 with a reserved Linux micro instance and 500 GB of EBS storage will cost more at about $60.00 plus the cost of the initial data transfer in.
A couple of months agao, I went through the same research as you and it is hard to beat S3 storage costs and ease of use. My requirements are more modest at about 100 GB per month though.
That said, there are too many ways to list here to check that any Apache server is secure. this Google search will get you started. http://goo.gl/SM9sB