One way to start on this would be one of the free power design simulators provided on various manufacturer web sites.
Since you mention Texas Instruments, try their WeBench Power Designer and SwitcherPro Design Tool.
While familiarizing yourself with these tools, you will understand the additional parameters that need to be defined for optimal selection of regulator.
To address specific points in the question:
- 3.3 Volt output: Easy to filter for, equally easy to specify as a parameter in the simulator
- Short circuit / OVP: Again, easy to filter for, use the parametric search on the TI site.
- Affordable: If you mean just the part, sort the parametric search by price. If you mean for the entire power regulation BoM, the simulators offer price as a design parameter.
- Efficiency: An LDO is less efficient than a switching (buck) regulator as it must dissipate the excess voltage as heat, proportional to the current drawn. This comes at the cost of increase in BoM line items and increased output ripple
Besides the above, additional parameters must be identified, such as:
- What is the source voltage?
- What is the maximum current that must be supported? Add a fair margin.
- What is the PCB area budget? If this is tight, a switcher might not be an option.
- What is the thermal budget? If heat-sinks are acceptable, LDOs or linear regulators will help with the "affordable" parameter.
- What is the input ripple expected?
- What is the output ripple tolerance? Switchers inherently have greater ripple, thus also additional output filtering capacitance required.
- What reliability requirements do you have? Greater MTTF comes at greater price.
- Do you need to handle extremes of EMI or power surges (e.g. automobile devices)?
Once these are nailed down, the selection becomes easier. These variables are the reason manufacturers like TI have such a vast selection of parts for fulfilling what is apparently the same purpose.
Further, this answer maybe of use to you.