I have a 1992 Bridgestone MB-4 that I am converting to a cyclocross bike. It is a 3 x 7 (21 gears). I am going to put down bars on it and to change the older over shifters and brake levers. As it is an old bike, I am looking to keep the cost down on parts. Does anyone have a recommendation of combined brake/shift levers that will work with 3 x 7? I have Deore XT rear and front derailleur. Any other suggestions/recommendations for this conversion are also welcome.
Integrated drop bar shift levers are inherently expensive, so I'm not sure how much you will be able to keep the cost down. Also, you will probably have a hard time finding 7 speed integrated levers. They would either have to be old, or low end. And even the low end stuff is quite highly priced. Based on the searching I've done around the web, it doesn't appear Shimano ever did 7 speed intergrated shifters above the Sora Level. When Dura-Ace and Ultegra were in 7 speed, they were still using down tube shifters.
Look up Shimano RSX brifters, 3x7 and compatible with your current derailleurs (any Shimano 7 speed should be). As @mattnz mentioned, they are often gummed up or jammed at this point in their life. If they are gummed up blasting them out with degreaser is a pretty simple process. Your LBS should know how to do this for you if you don;t feel comfortable. Another option is new tourney 7 speed drop bar shifters but those are junk. You'll have to stick to cantilever brakes. There's plenty of inexpensive high rise stems you can source from your LBS made by dimension or kalloy.
Additionally: as others have said, this is usually not really worth the time/effort/money. In addition to the new shifters, you will often need a new front derailleur, shift and brake cables, housing, handlebars, bar tape, and stem. Also, drop bars will change the fit of the bike, which could be accommodated to a degree with a shorter stem but you're sort of 'cheating' the fit of the bike.
All that said, if you're looking for a project, learning opportunities abound. drop bar mountain bikes can end up working out well. Just don't expect it to be much cheaper or easier than finding something on craigslist or saving up for a new bike.
With 7 speeds you can use bar-end shifters, that can be found used. The stem will need to be steep so it provides a big rise. Google for photos of drop-bar mountain bikes to see what I mean. Otherwise your weight will be too far forward and the bike will be hard to ride. I have a Spot Longboard 29" bike that I use drops on from time to time to change things up. Also, if the racing involves much portaging (carrying) the bike, that MB-4 might get heavy sooner instead of later. It is not and never was a high-priced bike, and allowances made to meet a price point equate to increased weight. Good luck, have fun.
Converting a mountain bike to a drop bar bike isn't a process that is likely to save money unless you are very careful with parts selection so you don't make mistakes, and spend a lot of time hunting for just-right used parts at bargain prices. Moreover, generally one would desire a larger MTB frame for drop bar use than for a standard MTB setup. However, people have had good results with such a project.
Note that you can buy a decent-quality 8-speed cyclocross bike for $400 from Bikesdirect, and you can probably sell your MB-4 for $150, which would make the net cost of getting purpose-built 700c cyclocross bike $250. That should be your max budget if you're trying to save money, as opposed to build a cool bike on a frame that has sentimental value to you.
If you're committed to this project, watch eBay and Craigslist for cheap 7-speed brifters & drop bars. But be prepared for the bike to fit oddly, and potentially to have a heck of a lot of seat-to-bar drop unless you have a really upright stem: http://www.cyclofiend.com/cc/2007/cc337-chriscullum0707.html (Note that bike has relatively little seatpost exposed for an MTB— you probably only want to attempt the conversion if you have a similar amount or less seatpost exposed)
I did this with an old '92 steel Univega frame. At first I put really cheap friction shifters on the ends of the bars, worked well for 7 bucks or so. I then found an old Giant Kronos on craigslist and got it for 50 bucks. Harvested the brifters, 7 speed and put those on, leaving the left friction to take care of trim. Added 26 x 1.5 road tires and new pads for the brakes. Works great and rides great.