Can I pick that specific artifact? Or is it a total crap-shoot in getting one when I get the points for it?

It's a crap-shoot. If you cash in at 5-6k it's 20% awesome. 60% useful. 20% crap. It only takes points for what you get. The more 'crap' you get the faster you can cash in. At some point you get enough points an hour that you get a pleasant little surprise every few hours. If you're still level 13 even the scrap value could be pretty high compared to mineral income.

It's better at higher levels since research is an inverse exponential return and artifacts are a linear return.. Not that I'm very high level.

Just get the best planets available (the oceanic).