The quality of resizing results depends upon the quality of the software you use. There is a lot of free software out there, but if you want really professional results in image manipulation, you really have two great choices for your needs:
1. Photoshop - horribly expensive and made basically unnecessary by the following:
2. Corel Paint Shop Pro - 99% of the functionality of Photoshop for 10% of the price. I have been a Paint Shop Pro user for >15 years. This is a very deep feature-rich program. I spent $25 for a book on how to learn it in 1 month with 30 lessons and that made me into a power user. Excellent image processing software has a long learning curve: you need to learn about compression, pixel structure, layers, masking, feathering, textures, etc. The more you dig into it, the more you love it and you can become an expert in less time than you imagine.
If you are poor and just can't afford the above, go to cnet.com and search for free image software. I am sure you can find something good. Pay attention to editors ratings and customer ratings and make sure it is not just a trial period, instead of unlimited freeware
You may not have access to free tutorials, though.
CNet should be your source for free software. It is way better than zdnet for that because zdnet is part of a huge publishing empire that is likely to steer visitors to their advertisers and their products more than CNet does. Either way brace yourself for lots of advertising and devious buttons to click.
Image processing and enhancement is so much FUN. I hope you find the tools that are right for you and that you enjoy using them as much as I do. Best wishes and good luck!