I've owned two JKs with a 3.8, two JKs with a 3.6, and now one JK with a 6.4. I'm betting the 6.4 wouldn't work for your budget. Of the other two choices, I would take a JK of any kind with a 3.6 over any JK with a 3.8. The 3.8 is painfully slow, and isn't even a fun vehicle to own. The 3.6 is pretty decent.
2017 Jeep Wrangler Rubicon Recon; 35s - no lift, Warn 9.5 XP-S, ARB Twin Air, SPOD
2017 Jeep Grand Cherokee Trailhawk (wife's Jeep)
2016 Ram Laramie 3500 Megacab 4x4; 6.7 CTD, Aisen, AEV Prospector conversion; 37s, 4.10s, Warn 16.5K