I'm a beginning racer/RC guy - started w/ my son doing 18th scale in Dec. 07. Now, we race B4 buggies and 10th scale cars. As for the 10th scale cars, I run NiMH packs and give up 100 grams to the guys with Lipo. They also have more out-of-corner punch and a bit more power at the end of a race than my NiMH. So, I say for on-road at club events, LiPo is a winner (nobody runs A123 but would be a possible benefit too). Now for B4 racing, at our local track, the fastest racer runs NiMH batteries - he runs a Mamba motor and drives well. Other guys run LiPo but off-road, seems like NiMh can keep up - since skill can beat battery unless you're really experienced or have a really large track which needs the extra power (the power output or "20C" rating of the LiPo). So, for example, if 4500mAh NiMH output at 10C - that's 45A output. If a 3800mAh LiPo output at 20C - that's 76A of continuous power. That's good for long straits and trying to add a bit more performance.
Benefits to NiMH - possibly lower cost overall but you need to watch for bad cells in packs and replace individual cells or whole packs if they lose a cell. Benefits to LiPo - power output, low weight, the new performance standard for most racing. LiPo problems - you need to be careful when charging. You need to know that LiPo can be "destroyed" if you go below their low-end voltage or if you overcharge and puff them up in size. So, NiMh can be salvaged if a cell goes bad but a LiPo pack may be deemed "done" if one goes bad there. NiMh pack new - about $30-50. LiPo pack new up to $100 for really good ones, even higher for on-road hard packs.
I'm going to keep with NiMh this season and into next until my son and I get better at our driving skills. Until we really need that added performance and drop in weight - we will hold off from going LiPo. A change to LiPo will mean - new packs for two sets of cars, two new chargers, unloading old chargers and packs on eBay, etc.
There really is "nothing wrong" from a realistic point of view in staying with NiMh if cost is an issue. Listen to your parents - if they really feel cost is an issue, respect that. Parents know when to put a hold on expenses especially if it's something that doesn't offer a huge benefit to you. If you are top-level racer who needs the LiPo packs, that's one thing. If it's just to get "the latest and greatest" - then it may be true that the change to LiPo isn't really the right decision at this time. You can have a ton of fun with RC cars without upgrading to LiPo.