I think you're doing this backward. Start with the target you want to shoot and consider what it takes to deal with it. Then pick a bullet that's designed to do the job (this is time consuming and requires some shopping) Then decide on a cartridge and gun combination. Then decide on a load manual and your components (like powders and primers.)
You can usually find out what powders are good by asking at a forum like this or by looking up the cartridge at reloadbench.com. Make sure you specify what bullet weight and type you are considering because that matters. If, for example, you plan to shoot varmint bullets in your .270, then you will not be using the same powder that you would use for a 140 grain bullet in the same gun.
You may find a really lousy combination of components, but if you do your homework in advance, then your problems and disappointments will be few. Just having a good manual-- like Speer #13-- is a big step in the right direction.
If you're shooting rifles for hunting, consider the temperature insensitive powders like the Hodgdon Extreme line of powders.
When a manual says use magnum primers, don't ask questions, just use the magnum primers. We're not artists here, just following a recipe that has been worked out by professional ballisticians. The magnum primers have qualities that make them better for igniting hard to ignite powders.
There's nothing wrong with Speer bullets. The manual is the best in the business. But don't limit yourself. Take some time to find out what you want to shoot, then work from there.
If you want to stick with Winchester powders, go to the Winchester website and take a look at their reloading data. Then compare it to what's in Speer #13 and make a choice. You can't be too far wrong using this approach provided that you have a powder that's reasonably suitable for the given cartridge.