To use a clause, an infinitive or a participle?

They're all fine, but the watchword for style manuals is "shorter". The participle shortens the word count and flows better.

Firstly, the first one is habitual and the last one is progressive, this is not a big problem with “to meet” due to the static semantics of the verb in this case, however with an active verb verb:

He is someone who eats rice.

He is someone eating rice.

The latter implies that the eating of the rice is currently in progress and the former is a habitual statement; the latter is in fact identical to “He is someone who is eating rice.”, but that sentence hardly flows as well.

A similar problem also occurs with the second one where with an active verb I would personally only use the infinitive for a past, future, or habitual event:

I am someone to eat rice.

Implies a habitual event, not a progressive one, but it can also be used for past events:

Neil Armstrong was the first man to set foot on the moon.

Neil Armstrong was the first man who sat foot on the moon.

*Neil Armstrong was the first man setting foot on the moon.

*Neil Armstrong was the first man who sets foot on the moon.

*Neil Armstrong was the first man who is setting foot on the moon.

So with past events, the infinitive or past form must be used.

This also follows with stative verbs:

He was someone who loved me.

*He was someone loving me.

He was someone to love me.

*He was someone who loves me.