I find the Military career the easiest to go up levels. No real hard requirements for the first couple of levels. By level four, you begin working only three days a week instead of four. Having the Handy and Athletic traits will help a lot as both the Handiness and Athletic skills are needed for promotions. Having a decent relationship with the boss is required as well.
To start, send your Sim to the Military Base to join the Military Career. If you have enough money, take the Handiness class at the base as well. Then, send your Sim to the Gym to learn Athletic by working out on one of the machines. The Gym also has shower and cooking facilities, so you can grab a meal or take care of Hygiene needs. Try to get a skill point in each on the first day, though you may not be able to get the Athletic point if your Sim is too tired.
In the morning, try to wake you Sim about 3 hours before their job starts (about 4 am for Military Sims). Send them immediately to the toilet and then the shower (baths take longer). Queue up a quick meal while you're at it. If your Sim has a partner, send the partner to cook a meal while your main Sim is in the shower. Do this every work morning.
Over time, you'll get into the habit of doing this without too many errors, but in the beginning it may be difficult to time your sleep properly. Start fulfilling small Wishes to build up Lifetime Happiness Points and (more importantly) Karma points. At 40 Karma points, you can activate Super Satisfy, which will max out all of your Sim's Needs. If your Sim has a partner, the partner can help build Karma points while your main Sim is at work.
That should get you started. As long as you keep your Mood and Skills up when you're working, you should reach level 5 without too many problems.
Flynn
