May a Baal Teshiva with no clear minhag avos or a convert accept any custom or reject any custom that thy wish? May a Baal Teshuva or convert for example adopt spanish and portguese custsoms, or minhag eretz yisroel , or teimani minhagim or any such obscure mesorahs so long as he is directed by a competent Rav?

ב"ה Shalom, First we should differentiate between a Ba'al Teshuva and a convert. Then we should say it would be inaccurate and irresponsible on my part to give a you an all-encompassing answer because there are so many variables to each case. There is no "one size fits all" in these cases as now follows. Though a generation or two of a Ba'al Teshuva may have neglected keeping Torah and Mitzvot, this does not mean that he is starting totally anew. According Rabbi Shlomo Zalman Oirbach, zt"l, the customs kept by our parent's parents (and beyond) are to be viewed as something they accepted for generations to come. (Halichot Shllomo Chapter 5) . The ramifications of this means that if your earlier Torah keeping generation was Ashkenazi then that is what you should keep, and if they were Sephardi that is what you should keep. However, even to this rule set down by Rav Oirbach zt"l , he himself makes the exception if a Ba'al Teshuva feels particularly close to a certain Rabbi and spiritual atmosphere which brought him close to Torah observance, he may keep the Rabbi's custom in, even if different than his previous generations, since it is like he was born from him. There are also further exceptions and variables to be considered by a competent Rav. In the case of a convert there is more room for flexibility, since he or she has no ancestors to follow. Therefore, at the onset he may chose the custom of his choice, but then he must adhere to it and keep one custom. It is even suggested by one Rabbi, that the Bet din should recommend that the convert should follow a certain custom conditionally, until he becomes more learned in this particular custom and other customs so he can make an educated choice which custom is closest to him, but then he must stay with one custom. (תפילה כהלכתה פרק ד’ סעי’ ה’ בשם הגרי”ש אלישיב זצ"ל) When choosing a custom the objective must be how to serve Hashem properly and how to become part of a community and the rest of the Jewish people. The objective is not to seek customs from the past or from distant communities, for which there may have been for specific reasons at a specific time which are no longer relevant. In any case, as you pointed out a Ba'al Teshuva or convert should always follow the guidance of a competent Rabbi so that he finds the way to truly come closer to Hashem. All the best