My best advice from a brief solo game I ran:
1) Minions are your friend, especially at really low levels. Otherwise, you'll be doing nothing but 1v1 fights which get old after a while. Makes the player feel heroic without overwhelming them.
2) Giving them minion allies gives you more xp to play with to make fights interesting while still keeping things pretty simple for you, and they still get to shine since they're way more powerful than their allies. Killing off minion allies can also ratchet up the tension abit without directly threatening the player, and can make fights seem close even when the player's character kicks butt:
Player: "Whew, that thing killed four city guards before I could put it down!"
3) Since combats can be really risky solo (if you're rolling bad, there's no friend who can hit a lucky streak and save the group), I ran a couple modified skill challenges using Stalker0's awesome
Obsidian system. He doesn't have an entry on the success table for 1 player, so I used 0-1 successes as failure, 2 partial success, 3 success - with challenges geared somewhat towards the player's strengths. This allows you to give xp to help her get caught up without the risk of killing her off due to unlucky rolling. Can also be used to restock minion supplies (see #2).
4) Stealth is your friend. When solo, stealth is probably
the most useful skill a character can have(though perception is right up there). Some character concepts just don't work with the sneaky, but if she has it, it'll help her start fights with optimal positioning to help skew the odds in her favor.
5) Avoid enemies that impose status effects and/or save-ends effects unless the she has some way to give herself extra saves(IE, paladins, clerics with lance of faith, the heal skill). Even then, a couple bad saves mixed with a daze, immobalization for melee types, etc can lock down a solo character pretty easily.
6) Defenders and Leaders will work best due to toughness/self heal abilities repectively. If she's not a leader, you might have her MC warlord or cleric, even if she retrains it later, just to have that extra heal if things are going badly.
All that said, 4th edition characters are pretty robust and it'll take most enemies at least a few rounds to put them down. As you said, even a wizard can survive if the player plays smart.
My 2 cents.
