To answer your question: there is no single answer. Even at our Mathematics department, for the first grade students, there are two professors of linear algebra, one uses $\bm{v}$ (bold math from bm package), the other one uses $\vec{v}$.
I would not use bar for complex numbers, because $\bar{z}$ often denotes the conjugate of $z$. I think that you should always make clear in the text whether you are real or complex.
Generally: In my opinion, you can use whichever notation you want, as far as you use it consistently in the whole work, and make clear (in Table of Notations in the Preface, or in the Introduction) what notation you use.
I don't believe there's a standard recommendation to answer your question, but it's probably not just a matter of personal preference either. A main criterion for good writing -- in any field, not just in mathematics! -- is the avoidance of all (unnecessary) ambiguity. One approach to keeping ambiguity low is to make sure that all symbols and notational conventions are explained at the outset. For instance, if you wrote something like
Let $\{\vec{v}_1,\vec{v}_2,\dots,\vec{v}_n\}$ denote a set of
$n$ elements of some vector space $V$.
in your paper, it should be clear to all readers that each \vec{v}_i, i=1,\dots,n, is a vector and that the subscript i merely serves to distinguish among the $n$ vectors. No further clarity would be gained, in my view, if the arrow symbol were shifted to the right to make it straddle both the v glyph and the subscript.
In contrast, suppose that the vector space V happens to be R^n and \vec{v} is some n-tuple. Now, there might be some ambiguity as to whether \vec{v}_i denotes the i-th element of v (i.e., a scalar) or the i-th n-tuple out of some set of n-tuples. If you need to refer to both types of variables in your paper, you might achieve a slight improvement in clarity by shifting the vector arrow to the right whenever you want to emphasize that you're dealing with an n-tuple rather than with a scalar.
To be sure, my recommendation in the second case would be to find a different notational solution altogether, in order to avoid any possible ambiguity. For instance, I might write v_i to denote the scalar quantity, i.e., I'd leave off the arrow entirely. I think that's much more direct and doesn't rely on your readers being alert enough to figure out on their own the meaning of a right-shifted arrow.
Best Answer
An important question to ask is, what do the subscripts represent? If "
sub" is of the formiorjand serves to index elements of the vector named a, it's customary not to typeset the indices in bold. Thus, you'd write\mathbf{a}_iand\mathbf{b}_j.If, on the other hand, "
sub" forms an integral part of the name of the vector itself, it's more common to typeset the subscript part of the name in bold as well. E.g., ifris the main part of the vector andaandsserve to distinguish sub-types ofr(say, for 'aperture' and 'screen'), you may want to indicate this property to your readers by typing\mathbf{r_a}and\mathbf{r_s}, respectively.Two final remarks: (a) As the preceding screenshot shows,
\mathbfproduces upright-bold characters. If you would rather generate italic-bold characters, load thebmpackage and write, say,\bm{r_a}. (b) Whatever you do in terms of vector notation, be sure to choose notational consistency.