The easiest thing to do is to play with an Existing Career, but I have problems with that. If you are trying to get all the Achievements on a minimum of 3 playthroughs, then you likely would want to start a new career (such as if you played a Soldier on Veteran, an Adept on Hardcore, and are now playing an Engineer on Insanity to get the tech. ability use achievements). Furthermore, I agree with Yezdigerd. Playing with a level 50+ character with Spectre gear and unlimited money is too easy; I would prefer something like a Mass Effect -> Mass Effect 2 import, in which you start with some extra gear, extra money, and an increase in level, but you don't have everything. Also, I would prefer it if you could change class type and background, but still get some perks for completing the game.
Here are great tips for Hardcore/Insanity:
First, travel to every possible system without landing on any planet/ships. Scan and survey all planets and asteroids. This will give you tons of cash, and minor experience. I use a pen-and-paper checklist to ensure I get everything possible.
Second, land on some planets and avoid the mission/assignment locations, and simply open probes, collect artifacts, and survery minerals. I recommend this second because you may still encounter enemies unless you are knowledgeable about the planets.
At this point, you will have tons of mods and equipment (but your level is likely to still be low, so they might suck), you will gain some decent experience, and you will have decent money. Just save your money and buy the best equipment (don't settle for mid-grade unless you have to).
Since you seem to be trying for the Ally achievements, and will most likely be using the same 2 team members for the majority of the game, develop of of the non-use tech members (Garrus, Kaidan, or Tali) to max. out their Decryption/Hacking/Electronics. When you cleanse an area of enemies, return with them to open any locked areas. Since you already dealt with the enemies, their combat skills are not needed, and simply opening locks with different members will not affect your Ally achievements.
Low grade equipment (I, II, III types) are best converted to omni-gel. They won't make you much cash.
Complete as many Citadel assignments as possible - most don't involve combat.
Talk to everyone, examine spots on the Citadel and the Normandy. Adding to the Codex gives experience.
As a biotic or tech-based class, simply save aboard the Citadel, use all your powers, and then reload the save prior to power use. Do this 75 times for each power, and you unlock achievements. In Mass Effect, achievements grant permanent bonuses to their corresponding powers across all playthroughs. Note that some powers must have actual targets like enemies or explosive barrels (Citadel Markets downstairs have 2 explosive barrels that return each trip).
For example, you're an Adept. Save your game. Cast Warp. Do not save. Reload game. Do this 74 times. You unlock an achievement, and Warp gains some type of bonus. You're are now tougher.
Want to cheat? Head to Therum as your first mission. There is a famous glitch here. As you get to the mining laser (used to access Liara's cell), enter A, X, B, Y. You gain experience. Save. Reload. Gain experience again. Repeat. You can also use the trick from above here.
If you do this the formula is: Use mining laser. Gain experience. Save. Use powers. Reload. Make sure to save before using your powers, as then you won't have to wait for cooldown. The game tracks your power use, even if you don't save after.
Next, complete Mako-based missions before foot-based missions. Attack using the Mako at all times. When shields are down, or damage is sustained, press X and return to the Normandy. Redeploy and re-engage. The Mako now has full shields, full health, and all enemies killed stay dead. This is a slow method, but it is faster than waiting for shields to recover. You also conserve omni-gel. Enemies remain damaged, but their shields will have regenerated. So what? Your focus is to kill just a few enemies each time, not to hurt every enemy a tiny bit. Plus, using the Mako's rocket launcher will make enemy shields worthless.
Remember to get as many achievements as possible on earlier, lower difficulty playthroughs because many enable benefits (getting 150 kills with different weapons, using biotic/tech powers 75 times, getting a measly 1 million dollars unlocks SPECTRE gear forever on ally plays, using medi-gel 150 times, these all make every future character better).
On foot combat, retreat, retreat, retreat. Take down one enemy at a time. Master defensive powers (Armor, Fitness, First Aid, Medicine, etc.), especially SPECTRE training. This skill is useful for many reasons, but Unity is one of the best abilities.
Go to Luna (Earth's moon) in the Local Cluster. Complete that mission, and gain a Specialization to make your character tougher.
Focus on just two allies, develop their equipment only. This will also help you gain ally achievements. Remember to create an ally just for opening locks (Garrus or Tali recommended).