What is a good, casual phrase to convey feelings of attraction and emotion without being vulgar,or too forward? I want to acknowledge someone as more than a friend, like telling someone you "like, like" them in English. I would like to say something that is somewhat romantic, but not sexual. However, I do not want to use anything that implies "love" because it is too soon for that.(I am very new to Spanish but it is my friend's native language)
If you want to sound somewhat romantic without further approach you can say
te aprecio mucho, I think it's a neutral sentence but it emphasize a friendship a little bit more, letting them know that you are starting to value the friendship more than just being simple friends but it welcomes the possibility to go a little bit further and start a strong relationship that can also be love.
Apreciar means you really care something without touching it.
Some sentences you can use:
(yo) aprecio mucho conversar contigo, creo que si sigo mejor ni te lo digo :P,
(yo) aprecio mucho tus consejos, significa mucho para mi,
(yo) aprecio tus deseos de salir adelante, haré lo que esté a mi alcance para ayudarte,
(yo) like in most spanish sentences is implicit thus not necessary and it's better to avoid it, I wrote it just for clarification but in real life, as I said early, it's not necessary unless you are trying to be really clear when you are making an anouncement.
Me caes bien.
This is always a safe choice. It can be the foundation of a deeper relationship, and spouses can still even say it to each other! But it's eminently safe because two mates will also say it to each other.
I'm not sure what would be a good way to document the meaning in context, but if you look at the usage examples in linguee.com, that might help convince you: https://www.linguee.com/english-spanish/search?source=auto&query=me+caes+bien.
This is a rather easy answer, and I hate to not have more to say about it, but there are basically two different ways to say such a thing.
Me gustas or Te Quiero
Me gustas is the literal way to tell someone you like them, and it carries the same weight as saying "I like you" in English does.
Te Quiero is a bit more endearing, though. It can mean: "I love you", "I like you", "I care for you", even literally, "I want you". This is not the same concept of "love" as the verb amar, though. It's like I said, endearing.