A step up from shared hosting is something called VPS Hosting which stands for Virtual Private Server, this is where the actual hardware of a server is partitioned so that each section can run independantly from each other but the individual partitions are part of the same server.
This option can be quite suitable and ideal for many webmasters as it is one step up from shared web hosting but not quite fully dedicated web hosting so it is an in between of those two services and can be quite affordable for most people who require that extra little bit without having to pay too much monthly.
It gives the customer some freedom and can mean that you are allowed to install scripts that otherwise would not be allowed on a shared hosting account, with VPS it will be running its own OS (Operating system) so that there is no worry of interference for the other customers as they too (as VPS customers) will have the same freedom from having their own partition of a physical server.
It has become quite a popular choice for customers, and as always it should be noted that just like shared hosting there are going to be some restrictions with VPS web hosting, but at least it offers those interested the chance to gain i guess what you could call semi-independance without it costing too much.
Each hosting company offering VPS hosting packages are going to have different rules in place of what they allow and what they will include as part of your package, for example you may find VPS hosting being offered by a company and you may want Cpanel as part of your package and the use of Cpanel may be seperately charged on a monthly bases so you will want to look into this and if you cant find the information on a web hosting company website then its worth asking just to make sure that what you will need or want with your VPS hosting account will actually be included, or if parts of the package are sold seperately then you need to count up the total cost of this so that you can see if you are getting a good deal with one web host compared to another.
The good thing with choosing VPS hosting is some of the choice that can be there for you and if this is what you need then it can workout just right for you and at an affordable price.
Have a look around and see what you can find, if you have been using shared hosting for a while and want to go one step up then VPS web hosting may be for you.