SimpleSimon, welcome! More memory will definitely help your situation. Here on this forum, we generally consider 2 GB of system memory to be the minimum for use with Vista. Your laptop has 1 GB worth of main memory installed. However, this GeForce Go series graphics chip has no memory of it's own. So, the graphics chip has to "steal" memory from the main memory. That 384 MB for the graphics is coming out of the 1 GB of installed memory! Thus, you are running Vista with 640 MB memory whereas we recommend 2 GB!
The Vista Home Premium that you are running is a 32-bit OS and thus has a limit of 4 GB of addressable memory space. Some of that memory is allocated to I/O devices -- more stealing -- so around 3.2 GB is the maximum that will be seen if you install 4 GB total. The graphics chip will steal another 384 MB bringing the total to just under 3 GB with a full 4 GB installed. If it can be done and would save you money, you could upgrade to 3 GB and after the graphics chip takes it's tax, you'll have around 2.6 available to Vista. That would be nice.
Keep in mind that even after a memory upgrade, the system you have is designed at a budget price point and is really not as powerful as it should be to run Vista. There would certainly be a performance increase with additional memory, but this system will still be slower than others running Vista. You can make adjustments by turning off certain features, but that laptop will always be struggling to run Vista. If all this makes you think that purchasing another laptop is the better option, do ask here or start another thread and we will advise you on what hardware will give you the best performance for a given price.