You can downsample. But you must understand that you inevitably will loose quality.
First because you take jpg pics, which are already a "let's act as if" solution as jpg reduces filesize by flattening differences between pixels. This loss cannot be undone.
Second because you will reduce the number of pixels dramatically (you'll keep one out of three/one out of four) and each pixel contains information that is either lost when you downsample in the 50%-25% etc scale as PS will simply discard one out ouf two/three out of four pixels) or approximated when you choose % that cannot be divided and hence have to be calculated.
And third because you're going to reduce the quality even more by resaving as jpg, meaning you'll flatten out even more.
I don't know how you see your own photographic skills (attention to dark shadows, ...) but it's always best to start with file that does not have enough contrast. Enhancing is easier that, say, trying to fill in burned out highlights.
Best is to take your pics also at the size for the web you intend to use, and then upload them directly as they were taken. These extra kB are normally not the problem.
So if you need to downsample, do it, in your case, in four steps, say, 1230wide, then 913, then 610 wide, then 400.
Use bicubic as that way PS calculates a mean value of all pixels surroinding every pixel, which gives best quality.
Otoh: many people don't see quality loss as visually it is not always obvious (depending on subject and other factors). But as you say you get bad results, it looks like you want high standard. In that case there is no easy way.
You can create an action for this as you're going to use it several times.
