Alright, here's a good starting sequence for a new psi character:
First, spend some SGSbucks on TK Punch and Temporal Distortion. Buy a Vigorous Belt from Pascal and then ask Ezra about Thought Control (or don't do this yet, and come back at level 3 and do it without buying a belt, if you want to save money). Talk to Quinton and persuade him to give you two free abilities in exchange for samples. Take his crossbow.
Go into the caves. In the first map after Jonas, skirt the northwest entryway and duck right in to that hide by the gate. Hopefully the rats didn't see you. If one did, just kill it. Now there's a closed gate between you and the rathounds. Take your time. Use a TK Punch to stun the rathound, then use the Putrefying Bolt with a 95% chance to hit. If the stun is resisted, you can try again in a couple turns. Again, there's a closed gate between you and the rats. You've got time on your side. Once you've tagged a rathound, kill it with TD stacks.
Once you've killed those two rathounds, you can go into the gated area, close the gate behind you, and manage the remaining rathounds in the map. Loot the buildings for oddities, ESPECIALLY if you're playing on Oddity XP mode. Then go back to Quinton and pay for Cryokinesis. Handing in the quest will level you up if you haven't already. Get healed up for free while you're there if necessary.
Now go back out again. Take the path south from Jonas' shack. Kill the crickets in the next two maps. Walk to Mushroom Cove. Use Cryokinesis to kill Cave Hoppers until level 3 (or, if Oddity XP, until you get the tail oddity, then stop grinding.). Hand in the hopper meat to Mordre. Go back to SGS to drop stuff off.
Go back out again into the outposts area where you started. If you've got stealth skill, stealth up right before going from the map you cleared earlier into the next map, using the west (up and left) exit. Whether stealthed or not, keep close to the wall immediately on your right (north) and walk over to the gate. The rathound there should see you. Stand right at the gate and *wait*. Should be three turns, maybe four, in combat. Suddenly, rats will pour out of the opening south. Open the gate, walk through, and close it. While they run back around to try to get to you, run into the building ahead of you and close the door behind you. The south door leads into a gated nook. Go there, and safe from harm, kill the rathounds at your leisure. Insert the flux controller, loot the shelf for the oddity, kill the two rathounds past the gate to the north and power up the outpost. If you weren't level 3 before, you are now. Go back to SGS.
Use one of your freebies to learn Pyrokinesis. Go back into the outposts areas. Go north from the screen you were at in that previous paragraph. When you pop around the corner, ice spear the rats and back into that little corner nook. When the rats come close, Pyrokinesis to make the run in fear. Pick them off with Cryokinesis. Do not blow the barrel.
Open the gate. Walk to the door and open it. Back off a touch. When a rathound walks into your LOS, kill it and haul ass to the gate. Close the gate behind you and get out of LOS so Whathisface McDeadface has to open the gate. He'll walk right up to the giant Barrel of Death. Cryokinesis to blow it up, killing Stupid McDead and his dumb stinky dogs. Power on the outpost and loot stuff. Take the elevator down. Loot the lockers and leave to the east (down and right).
Take the first ladder. Hack the box and loot the shelves. Pick the door. Manually engage turn based mode after you walk out the door and walk around the corner to get that one rathound by itself. Kill it. Make some noise to pull the two near the gate, or open the gate, walk out, pull with cryokinesis, and walk back in then close the gate. Clear the map using the gate as your safety net.
Before doing Hopper Round-Up, talk to Jack Quicksilver and accept his quest. Buy one frag grenade from Lucas if you don't already have one. If you're level 4, pick up Electrokinesis from Bisson. Go get the package and kill the three stooges. Go down into the Underpassages. Carefully clear out the four Lurkers in that map. Leave to the east using the more northerly of the two exits. Manually engage turn-based mode before walking around that big scary corner, then TK Punch the Lurker in the Aluminized Tac Vest. Go deal with the stealthed guy and kill the rathounds behind the locked north gate. Loot the riot gear. If you feel like it, open the other locked gate and kill the Lurker with the AR.
Now you can take some hits because you've got DR. Go kill three screens' worth of rathounds. In the northern one, pick the gate and hack the boxes to get loot. In the western one, kill rathounds either using the door or the gate as your safety net. Turn in Jack's quest.
Go do Hopper Round-Up.
The game will be much, much easier from here on out, because you'll be level 6 and will have Premeditation. You still can't just facetank the world, but you'll have tools available (four-turn Force Field, Premeditation, AoE psi abilities, stuns) to get you through the problems.
Have fun =)