I wouldn't do much with it immediately. However, going to the energy vendor and buying an extra weapon slot for a bomb would be a good. As a new player, you should use sword, gun, and bomb on a few runs to see which you like best. The weapon vendor in the bazaar always has a nice selection of beginner bombs, or you can get the Blast Bomb recipe from Kozma and start yourself on an upgradable path.

Play the dungeons a bit with your proto gear and make sure to try all three weapon types to see what you like. If you want to play more than your mist allows, use the 10CE per elevator to enjoy more dungeons. I think it's well worth the price. Playing is fun!

After playing a bit, you'll get a feel for what you want. If you want a better weapon first, either find a recipe you like from Basil or Kozma (the recipe vendors) or buy a premade weapon in Haven Bazaar. Same goes for shield, armor, and helmet. Eventually you'll need 2* gear to get yourself into Tier 2, but don't worry about that too much until you've mastered playing in tier 1.

If you are still unfamiliar with playing Spiral Knights. One of the biggest mistakes made by new players is raising multiple times while learning to be more skillful. You can easily lose ALOT of that energy on multiple raises.

As a new guy, while running levels, don't revive if the cost to do so would be more than the elevator cost to reach that level.

It's not the best rule possible, but it's a start.

I strongly support the advice to NOT revive too much. Setting a minimum cost is one good criterion; another is to not revive if you think you'll die immediately. Try to adventure in a party: then other players can use their health to revive you for free. (and you can help them!)

Weapon slots are nice, but starting out, I made the mistake of buying the slot before I had 3 weapons. That was not a good value for the money.

The best thing to spend your energy on initially is to play the game: adventure a lot. You'll get crowns, and materials, and learn basic skills while seeing gear in action. Then, as you've learned more, you'll naturally develop a list of the things you want to spend money on. (and the things you don't) Done right, your $10 can last a very long time.

Other advice:

• Don't sell energy for crowns right away. Spend the early days learning what you want to get (check the wiki, and talk to other players)... by the time you know what you want, you'll have the crowns to buy those early recipes (and the materials to make them!). This will save you money by avoiding false starts on items that you turn out not to want, or that don't have upgrade potential past 2-3*.
• Know the actual prices of items and recipes ( http://wiki.spiralknights.com/Crafting ). A lot of "trade" offers I've seen lately are terrible deals: some players will try to buy energy for crowns at far less than the exchange price, while many others are selling 2* recipes for 2-3x their cost. (The markup on other recipes is similarly very high)
• When buying materials... if something seems expensive, try to meet the seller in a crowded public area and discuss prices where others can hear. Someone may step in to tell you it's overpriced. Don't fall for high-pressure sales tactics: if one person is overcharging, there are LOTS more potential sellers out there, and many are desperate.
• When buying materials, price things in crowns, and ALWAYS check the current exchange price when paying in energy instead. Prices change overnight- sometimes dramatically. Don't pay yesterday's prices. :)

Don't play like you have unlimited energy. For example don't rez if it's over 10 energy. Or 5. Definitely not over 10 though. Don't buy things unless you plan on using them immediately. Don't stockpile recipes to use for later. Don't buy mats to use for later. Don't do like i did (not knowing what my noob self was doing) and craft 4 different tier 1 swords, lol. Just little things like that. Play conservatively, that energy is only gonna appreciate, and when it's gone you'll regret what you wasted.

Which also is why i agree with skipping 1-star gear. Go straight to 2. Buy it at a discount. If your curious, make a post hear asking what you should be willing to pay for XYZ equipment.