Website Hosting Package advice

We have an internal website developer with little experience of hosting packages.

Based on the following specifications he has provided could someone please recommend suitable hosting packages:

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PHP requirements:                        PHP 5.3 or higher
MySQL Requirements:                 MySQL 5.0.4 or higher
Server:                                              Linux/Apache 2.x or higher or Windows IIS7
There’s arguments for and against both Apache and Windows options but based on our experience previously, Linux was the more successful of the 2.
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Backup

We would like a fully managed backup which ideally would be restored for us in the event of a major failure.  However, we would also like the ability to take our own backups using Akeeba v3.6.9 which we have done so for the test site.

The web designer has used Joomla Version 2.5 to develop the website

Currently we have the test site on a Linux Server with 123-reg which is a basic package and often seems slow considering the lack of traffic and does not have any backup services attached to the package.  

I have attached a few screen shots of the traffic for last month and for the last 12 months.
last-Month.JPG
last-12-Months.JPG