Should I choose the smallest datatype possible, or if I am storing the value 1 for example, it doesn't matter what is the col datatype and the value will occupy the same memory size?
The question is also, cuz I will always have to convert it and play around in the application.
UPDATE
I think that varchar(1) and varchar(50) is the same memory size if value is "a", I thought it's the same with int and tinyint, according to the answers I understand it's not, is it?
Always choose the smallest data type possible. SQL can't guess what you want the maximum value to be, but it can optimize storage and performance once you tell it the data type.
To answer your update:
varchar does take up only as much space as you use and so you're right when you say that the character "a" will take up 1 byte (in latin encoding) no matter how large a varchar field you choose. That is not the case with any other type of field in SQL.
However, you will likely be sacrificing efficiency for space if you make everything a varchar field. If everything is a fixed-size field then SQL can do a simple constant-time multiplication to find your value (like an array). If you have varchar fields in there, then the only way to find out where you data is stored it to go through all the previous fields (like a linked list).
If you're beginning SQL then I advise just to stay away from varchar fields unless you expect to have fields that sometimes have very small amounts of text and sometimes very large amounts of text (like blog posts). It takes experience to know when to use variable length fields to the best effect and even I don't know most of the time.
The advantage is there but might not be significant unless you have lots of rows and performs los of operation. There'll be performance improvement and smaller storage.
It's a performance consideration particular to the design of your system. In general, the more data you can fit into a page of Sql Server data, the better the performance.
One page in Sql Server is 8k. Using tiny ints instead of ints will enable you to put more data into a single page but you have to consider whether or not it's worth it. If you're going to be serving up thousands of hits a minute, then yes. If this is a hobby project or something that just a few dozen users will ever see, then it doesn't matter.
Traditionally every bit saved on the page size would mean a little bit of speed improvement: narrower rows means more rows per page, which means less memory consumed and fewer IO requests, resulting in better speed. However, with SQL Server 2008 Page compression things start to get fuzzy. The compression algorithm may compress 4 byte ints with values under 255 on even less than a byte.
Row compression algorithms will store a 4 byte int on a single byte for values under 127 (int is signed), 2 bytes for values under 32768 and so on and so forth.
However, given that the nice compression features are only available on Enterprise Edition servers, it makes sense to keep the habit of using the smallest possible data type.