- Install on a single server with built in DB : This installation is a good platform for learning and testing. It installs SQL Server 2008 R2 with SP1 Express edition. Which means you cannot go beyond 10 GB for database size. You can download SharePoint Foundation which is a free edition and use this model to install it on a personal computer.
- Install on a single server with SQL server : Using this model you can install all the components of SharePoint on one machine. Advantage here is that this model is scalable and you can use full version of SQL where is no 10 GB restriction on DB size. Microsoft do recommends not to go beyond 200 GB for one content DB. I will talk about this in a different article.
- Multi-tear installation: This model usually consists of web, application and database layers. There could be multiple servers on each layer sharing the requests and load. Web tier consists of WFE servers which directly respond to customer requests. Application layer consists of search and service applications. DB layer consists of SQL server hosting config, content ,etc databases.
- Hosted solution from Microsoft : I have not personally used this model. More information about this can be found at SharePoint Online.