This kinda thing starts moving into the grey area of what you can do on web hosts while abiding their Terms of Service. Most shared hosts require that your stored content be used at your hosted website (and not simply as a repository for use elsewhere). They have to demand this or their services would be quickly abused by file storage and bandwidth beasts.
One way you could approach this is to setup a gallery and host your images on it, then hotlink your images on your myspace page. This way you're using the content at your domain and remain within the boundaries of the TOS.
For the job you mention, free image hosting sites such as PhotoBucket and TinyPic might provide an ideal alternative and require little to no setup. For one-off images posted to a forum, etc. tinypic is a good choice. If you want to collect your images in a gallery-like folder structure under your own account for archival purposes then you can create a free account at either of those places.
If your images are for prosperity, take a look at installing Gallery on your domain right here. It's a pretty good application and is available as a One-Click Install too. More importantly, at least one of the regular posters here (Scott) knows a lot about Gallery and can offer advice if you run into any problems.
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