Having done this twice, both as a DM and as a Player, I have to say from my experience: DO NOT ALTER THE RULES AS GIVEN.
And definitely: DO NOT PUT YOUR PLAYER UP AGAINST ANY NPC WITH MORE THAN 150% OF THE PC'S EXP. For first level characters, that means 150xp max. Yeah, I know what you're thinking - limiting, very limiting. However, under 4E, anything else you're looking at a TPK.
For example, to let you know how stringent this 150% rule is. As a 1st level character, I went up against an NPC worth 175 exp. I could never beat him in a straight up fight one-on-one. If you're interested, I was playing the pregen Warlock vs. the Human Mage from the fan monster manual off these boards.
Now, I know where you're coming from, soloing in any other edition was a stone cold migrane. But, amazingly, it actually works pretty well in 4E without major changes to the rules. Of course, you won't be fighting as many monsters as a party will, but believe me, blowing away a group of four Kobald Minions with a single Scortching Burst has a sort of visceral appeal.