If you want to turn a small budget team into a large budget team, ignoring budgets is fine.
However, you can still be competitive with budgets turned on. You just have to be smarter with your money. If you rarely sim, don't be afraid to lower your rehab budget, as you will not see many injuries on the MLB level in games you play. Also, try to find the most profitable way to run your stadium and vendors. A good guide on that can be found at
http://www.gamefaqs.com/console/ps3/file/937279/47228. (Yes, this is for MLB 07, but most of it still applies)
Also, the draft is your greatest asset, so don't be afraid to spend more on outstanding scouts. Since you will want a steady stream of A/B potential guys in your farm system (home grown talent is cheaper), you will want the most information on draftees as possible.
Finally, the Rule 5 draft is your best friend. If you have a few guys on your squad in the last year of their contract who are owed a lot of money, trade them away for prospects, and look to the Rule 5 draft to fill in any holes in your MLB roster.
It is a lot of work to be competitive, and usually takes more time and effort, but small market teams can be a lot of fun to try to turn into true powerhouses.