I already live in a house owned by a Jew - can I purchase it during sefirah or should I wait? I am under no special pressure to purchase now or lose the opportunity.

Shalom, Thank you for your question. There is no restriction on buying a new house during the omer period. (The restriction on new purchases is found during the mourning period of the Three Weeks leading up to Tisha Ba'Av – but not during the Omer period). I attach for you here an answer to a similar question that was asked about purchases during this period. Thank you for your question. First let me clarify the laws of buying new items and saying the blessing "shehecheainu" during the days of Seferat HaOmer. According to the general consensus of Rabbis, there is no prohibition at all during the Omer concerning buying new cloths or saying the blessing. All the major authorities (such as the Mishna Brurah and others) rule that it is perfectly acceptable to say the blessing "shehecheyanu" during these days. The common idea that there is such a prohibition probably comes from a confusion between the Omer days and the three weeks before the 9th of Av. Based on this, the answer to your question is quite easy – you may buy anything you like during any of the days of Omer, and use it immediately, even if it requires the "shehecheyanu" blessing. However, there is a minor opinion found in some sources (see Piskay Halachot 493, 2-3) that mention a custom to refrain from both "shehecheyanu" and buying new items during the Omer. As this is not the main, accepted opinion, my advice is that you should not follow this view unless you have a family or community custom to do so. Even then, because it is only a custom, (and a debatable one at that), it should be applied in the most lenient fashion. This means in all cases of doubt you should rule that it is permitted. So, in the case you asked about, it would be permitted (even according to those who are strict and refrain from buying new things during the Omer) to buy them in a case where they will be delivered during a non-mourning time. More than this – I would go so far as to say that one may in fact buy new things during this period on the condition that you do not use them, or wear them, until the permitted days. In conclusion let me reiterate that the normative halachic approach is permit buying new items, and saying "shehecheyanu" during the Omer days. In general that it the opinion one should follow. Blessings.