Well, I personally have never played the basic set, but I have read a bit of it. It is aptly named in that it's a very basic rules set. I'm not sure of the makeup of your group, or where you guys are playing, but if you have access to it I'd suggest maybe trying out 4th Edition D&D. Myself, I prefer 3rd Edition but 4th might be better suited for you guys. From reading the 4th Edition system, and from listening to others here on ENWorld, it seems to be a very easy system to learn and play, and would have a lot more options for you and your players. The 4th Edition Dungeon Master Guide is absolutely chock full of awesome, yet easy to understand, advice for both beginner DM's/GM's (Dungeon Masters/Game Masters - both mean the same thing) and veteran DM's/GM's. The three book box set for 4E would probably cost you around $65 online.
If buying more material or moving to another edition is out of the question, for whatever reason, then this is an example of "if the rules are getting in your way, ignore them or change them". In other words, if the RAW (Rules As Written) of the set you are using doesn't work for you guys, change it. Now I know that may sound easier than it is, I'm sure you don't want to fiddle with the rules and then possibly create other problems. So, here are some houserule ideas for you (houserules are rules that groups and DM's make up for use in their own games).
- Make attack spells (like Magic Missile) an at will spell for Wizards (rather than he "fires and forgets"). In other words the Wizard can cast it whenever he wants, just like a Fighter can attack whenever he wants. But, you'll need to change the spell to no longer always be an automatic hit. Have the Wizard make an attack roll using his Thac0, to see if he hits. If the Wizard seems to be having too hard of a time ever hitting with his Magic Missile using this idea, try having the Wizard use the Fighters Thac0, but only for magical spell attacks. You could even make this not count against the number of spells he has or memorizes, it's just a "Power" that the Wizard always has (this is basically how 4th Edition, or 4E, does it).
- Adapt rules from another edition or ruleset. Unfortunately, spell progression is the same in 1E, 2E, and 3E (1st and 2nd Edition Advanced Dungeon's & Dragon's {AD&D}, and 3rd Edition Dungeon's & Dragon's), however, spellcasters also get bonus spells based on their Intelligence score, and in 3E can also cast 0 level spells (also known as Cantrips). You don't have to buy the books for 3E though, the rules are "Open Content". 3rd Edition rules are all availabe for free as the D20 SRD (or System Reference Document), the best source is here.
There are also some Open Content rules systems for Original D&D and AD&D style play that are supposed to be very easy to use, available at places like
RPGNow.com - The leading source for indie RPGs and right here on ENWorld at
ENPublishing. Someone else though would have to give you advice on which ones might work the best for you since I really haven't read or played any of them. (I believe one such system is called OSRIC. OSRIC stands for Old School Reference and Index Compilation.)
I hope this helps a bit. For more specific DM'ing advice, just post your questions here. I, and other ENWorlders, will be more than happy to help out (the people on this site are really good about doing this).