You're right about the lack of Fire types...Ponyta is the only one before you beat the Elite Four and/or get the National Dex (you can get the National Dex before you beat the Elite Four, despite a lot of rumors), aside from Chimchar of course. Honestly, I couldn't give you a completely accurate answer on whether it would be a bad idea or not. I myself picked Piplup for my Diamond Version, but I also got Pearl on release date so I sort of cheated and got all three starters to start out with. I know, I know, but I just couldn't pick between the three. Grass Type which I used to always start with, a fire monkey, or a penguin. Piplup was my starter, because I finally decided that if I had to choose one, it would be Piplup. Not exactly the most sensible decision-making process, but another deciding factor was that after calculation, I realized that Empoleon has the least amount of weaknesses, the most resistances, and thus is a smart choice.
Anyways, since I had Chimchar as well, things were much easier. I didn't face the problem of a lack of fire types. But I must say that, as I previously mentioned, Piplup is, in the long run, a very smart choice. So I wouldn't necessarily say it's wrong.
If you really don't like the fact that there's Ponyta as a fire type and that's it, I'd be very willing to trade just about any fire type you want to you. If you feel like that would be cheating too much, I understand, though.
Also, if you did want one but you wanted it to have you as the OT, I could trade you an egg so you are the OT. PM me if you're interested. (PS: I don't need a great Pokemon in return, it wouldn't be that much trouble for me to fetch a fire Pokemon so you could give me something like a Bidoof and I wouldn't mind)
All in all, it is a little troublesome, the lack of fire types, but if you're thinking of resetting your game and starting with Chimchar, I wouldn't advise it. There are other types you can use to combat what fire normally would, there are Pokemon like Skuntank that can learn fire move(s), and the team you go through the game with will most likely not be the team you actually use in reality, so it's not a big deal if you don't have a fire type to start.