rocker86, the ONLY way to ensure rows are returned in a specified order in any relational database is to use the ORDER BY clause. This sorts in Ascending or Descending order based on the collating sequence of the code page the database is using.
In your example, it would be impossible (to guarantee) the returned data will be in the same order as your Link_Order table as it is not in any sort order. If you used an ORDER BY the first column, Jim would be first, Mike second and Tom third. If you used ORDER BY first_column DESC, second_column ASC, the first column would be in order (Tom, Mike, Jim) but the second column would not (and it wouldn't matter if it as ASC or DESC). You would have either tom_fifth, tom_first, tom_fourth, tom_second and tom_first or the reverse of that.
To answer you other question (what order does a default Select (one without an ORDER BY) fetch rows), the answer is whatever order the database engine finds them. If you have a Clustering Index (and your data actually could be sorted in an order you wanted) on a static table where nothing changes and you do a SELECT on just the one table (and the table has been Reorged to put the data in clustering order) without a WHERE clause (or at least one that only references the columns in the Clustering index), ORDER BY, GROUP BY, DISTINCT (or anything else that could cause a Sort), the rows will (most likely) be returned in the Clustering order. This is because the data will (probably) be accessed by a Table Space scan reading the First Page, First row, second row.., Second Page, next row, etc.
Since the data is in clustering order it would be returned that way. But almost ANYTHING could cause that not to happen. If you Insert or Update the Clustering Key value, the rows affected could be put back into the table on ANY page (i.e. not in Clustering Order) and the same table space scan would NOT return the data in the actual clustering order. If a index RID sort is used the order of the rows being returned can be affected. Anything that causes a sort can change the order. The amount of data in the table could change how the data is returned. This list could go on for quite some time of the things that could affect the 'default' (there really is not such thing) order the rows are returned.
So, as r937 has already stated, If you want you data sorted and it can't be sorted based on the collating sequence, then you can NOT order your data (even with an ORDER BY clause). Your only option is to include a column that CAN be sorted. Since you stated this is not an option, you can't do what you want to do.