Nothing should happen to your installed applications and files. Seems to me you may be lacking RAM, something you need to address if upgrading. Here are the steps to take if all is basically well.
Before buying anything you should first make sure your machine will accept the upgrade you have in mind.
Minimum specs for Snow Leopard. Mac OS X v10.6 Snow Leopard -Read the Technical Specifications
From the USA go to http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
In Europe or otherwise substitute your national code in place of /us above.
In the UK … the last known price was £14.
Before you start upgrading, back up your files.
Once you've upgraded to Snow Leopard you will need to apply the Combo updater. Mac OS X 10.6.8 Update Combo v1.1 and follow with a software update to pick up any additional updates.
In the long run you may save time by simple erasing your hard drive and then install Snow Leopard. Get an external drive to backup your current system. First make your backup:
Clone using Restore Option of Disk Utility
1. Open Disk Utility in the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Select the destination volume from the left side list and drag
it to the Destination entry field.
5. Select the source volume from the left side list and drag it to
the Source entry field.
6. Double-check you got it right, then click on the Restore button.
Destination means the external backup drive. Source means the internal startup drive.
Then boot from the Snow Leopard DVD and do the following:
1. Boot from your Snow Leopard Installer Disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu.
2. After DU loads select your hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Note the SMART status of the drive in DU's status area. If it does not say "Verified" then the drive is failing or has failed and will need replacing. SMART info will not be reported on external drives. Otherwise, click on the Partition tab in the DU main window.
3. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Partition button and wait until the process has completed.
4. After formatting is completed quit DU and return to the installer. Install Snow Leopard.
I don't know how old your model is, but the earliest Intel-based Mini could handle 2 GBs, so at the least you can upgrade memory should you wish to do so. If you decide to do that then I recommend visiting OWC or DataMem to determine what type of memory you need to purchase. Both are highly reputable memory purveyors in the US.
If you aren't in the US, then you will need to use Google to find out who vendors are in your neck of the woods.
Maximum Memory 3.0 GB (Actual) 2.0 GB (Apple) Memory Slots 2 - 200-pin PC2-5300 (667MHz) DDR2 SO-DIMM
You can install two 2 GB modules. However, because of the controller only 3 GBs will be available for use.
You should visit OWC where they should have tutorials on how to install the memory.