There's a market place. There are two options. Providing request for registration to surf marketplace or not request for registrations. In the second case we have 25% more sales more but number of registrations arу reduced by 3 times. What is more important for startup, while marketplace seelers need sales right here and right now?
I'm not clear on the question - so this answer may not fit. If the goal is to get 100% registration of those that purchase, then keep your current strategy and add registration at "purchase" time as well. If the person went through the second case (no registration) then use the action of purchasing as a mechanism to register. The goal of registering is to gather customer contact information. Your customer database are leads to future sales and services. Once again - I'm not 100% clear on the question. So this may not be answering your question.
This is a good question and always pops up in many projects. We always try to look at the customer life time value as the long term KPI. In most businesses 20 % of your valuable customers account for 80 % of the overall sales. It helps to identify those customers, by setting up a clear funnel analytics over a longer period of time and measure each conversion step.
: from visit to registration, to sales, to repurchase and so forth. Also take into account the value of each sale. A customer that had to register to purchase, has shown a bigger commitment and might become more valuable in the long run. Many times it is quite easy to get registrations, what counts is the sales. On the other hand with registrations you have a valuable database you can retarget potential customers. I guess you should try, analyse the results and continuously optimize. Moreover this also depends on your kind of product and the traction you want pursue.
Just look at your ROI return on investment. You should clearly see which way is going to get you the most money the fastest. If you could some how do both methods that would be the best option.