Don't bother looking into Eureka. Even if you had the raw time to invest in its already impressive time sync, and you had someone to guide you every step of the way, the logograms alone would do you in. Last I checked, you'll likely dump 2-3mil gil buying what you need off of the market board. If you were to farm them yourself, you're talking about already adding a potentially excessive amount of time to the experience.
Eureka is for glamour. Not a smart option given your current restrictions.
You could try and run Heaven on High for the weapon. At 70, you'll get tomes of Mendacity and Genesis to work towards your weekly cap and buy ilvl 390 stuffs - and the empyrean weapon you can get from there is ilvl365. If you are lucky, you'll get drops that sell for decent amounts. However, that can get really monotonous in a hurry.
As for what to buy first with Genesis - I usually go for jewelry first, because they are the cheapest at 375 a pop.
