Well, I’m already assuming you own some good white and blue dress shirts (I’d personally recommend getting those basics first, as they’ll be more versatile), and looking to add some variety.
I’m not entirely sure what context you’re looking to use the dress shirts in — with suits? with sport coats? with sweater vests? with waistcoats?, etc. — because I think that matters as well. I have a set of shirts that I typically wear with my suits and another set that I wear with sport coats/blazers as well as more casually.
For suits, I’d toss in a pink shirt and a lavender shirt. Some people like ecru (yellow-ish), but I’m not personally a fan. I think pink adds some vibrancy to your face if you’re fairer skinned. Lavender also looks nice, in my opinion, and ads some colorful pop to a suit without being overly aggressive if you tone it down with a darker necktie (or you can contrast it up like I did yesterday).
As for patterns, I’m a big fan of gingham prints, but I don’t typically wear them with suits (although I kind of broke that personal rule of mine yesterday). Gingham looks great though and can be really bold when used with bright colors (purple, red, blue).
As for striped shirts, I prefer to wear those more casually, but that’s just me. I think a thin, pinstripe maybe spaced .25” apart looks simple on a white shirt. I would try to avoid multi-colored stripes on a shirt, as I think it looks too busy.
For oxfords, I think the university stripes look great and adds some variation to the typically solid-colored shirt.
I know others really like plaids, but I’m not entirely fond of them and would only wear them in a very casual context.
The most important thing though would be to really nail down what looks good on you. You could buy shirts in every color of the rainbow just to have variety in your closet, but I’d honestly wonder how well it would go with the rest of your wardrobe and ultimately look good on you.
Maybe there’s color that looks good on you or a hue/shade that is more your style. Maybe you do better with darker shades, or lighter shades, or maybe you switch those up based on the season.
Once you get an idea of what your personal style will be, I think the next step is seeing what helps add to that in a positive way, and following that path. See what you like, what you have and work from that. It’s not so much about colors and patterns, but what you want your style to be.
I hope that made some sense?