In addition to what he said, increase your stitch length when sewing on leather so you do not create to perferated a line of stitches that your leather pulls apart.
As for the sewing machine, depending on the model Kenmore you have (if the model number starts with 158, score!), it may be worth having it serviced. They are workhorses and tend to handle most fabrics with ease. Plus, you can get roller feet and teflon feet for the Kenmore at a reasonable price.
Berninas are great machines, as are Pfaffs, Janomes (which I think are the current makers of Kenmore), Viking, and upper-end Brothers (not the models sold in big-box stores).
What Katpac said. Also, make sure your bobbin thread is unwinding across the top of the bobbin, not from below, when inserted into the bobbin holder, and that it is caught in the tension guides. Also, make sure the bobbin assembly is inserted all the way into the machine (which you are probably doing, but sometimes simple things are the easiest to overlook).
There are circle guides (purchased and hacked) that will allow you to sew perfect circles, but I do not know of any guide that will sew the curve for you. Using a seam guide may make it easier to get a precision curve..
Most good, mid to upper end of the line sewing machines will handle the types of applications you want to do with your next machine. You will not find these machines at one of the big box stores, but at a local sewing machine dealer who will let you sit and try out their machines before you buy.
When selecting a machine, take fabrics you intend to work with. They will let you use them and not just their heavily stabilized sample fabrics. If they do not let you test their machines on your fabrics, find another dealer.
A great alternative is, as another poster suggested, a vintage machine. The workhorse of the 60's and 70's is the Kenmore line that start with the model number 158. If you keep an eye out, you can find them easily at thrift stores and yard sales. Check it out thoroughly to make sure the motor works, that cords are not freyed, that the accessories come with it (bobbin assemblies, accessory feet, cams if the machine accepts cams, button holer attachment, etc). Depending on the condition of the machine and your negotiating abilities, you may be able to pick it up for $10-15 dollars, well worth the risk and the cost of professional servicing. These machines do not wear out and, even if it does not come with the accessories, you can find them regularly on Ebay and shopgoodwill.com. The feet are standard feet that can be easily replaced through Clotildes or even Sears.
Another tip for sewing on heavy fabrics is to use adding machine tape on top of and underneath your fabric. It can help the machine feed the fabric through the feeddogs. You can also use strips of tissue paper (the type used in wrapping gifts, not the bathroom type). The stitching will pierce the paper and you just rip it out after stitching. Any paper remaining will not affect the seam.
If your machine has a presser foot pressure adjustment, try adjusting it up or down to see if that helps.
You might also want to look at the Kenmore brand line of machines. I think they are currently being manufactured by Janome. Kenmore has had a good reputation for support (I was able to get a part for a machine made in the 60's!) and I picked up a relatively new Kenmore at an estate sale to use as my class machine (instead of lugging my very expensive Pfaff around) and it is a very respectable machine. Plus, you can get feet for the Kenmores at a reasonable price (around $10 as opposed to $25+ for the Pfaff).
Rethread your machine completely, including the bobbin. Make sure your bobbin is correctly inserted in the bobbin holder and the thread is running through the tension guide. Make sure you are using the right size needle fo the fabric, and that your needle is new or only has a few hours of sewing on it.
Clean out the bobbin area and holder, paying special attention to where lint can build up and pack down. You may also need to put a drop of oil in the bobbin area (check your owner's manual to find out where! Then run waste fabric through to clear up any excess oil).
Once you have done the above, run fabric through your machine and check your tensions. If you have a bobbin that is under the machine (as opposed to a drop-in bobbin) a simple test of bobbin tension is to thread the bobbin holder and, holding the thread give it a little jerk and see how far the bobbin assembly travels down the thread. If the tension is good, it should only travel about 3-4 inches. If the bobbin assembly travels a long way, tighten the tension, if it barely moves, or moves only an inch or two, loosen the tension.
Sergers are built to sew and trim the seam at the same time. Practice on scrap to make sure your tensions are correct and you are stitching the seam stitch on your seam line. The 3/8 inch seam allowance is really for a traditional sewing machine seam. You can get by with a narrower serged seam (assuming you are serging with a 4-thread serger, if you have a 3-thread serger, see below). The main thing when you are seaming with your serger is that you are seaming on your seam line. Until you are comfortable with siting your seams, you may want to mark along your seam line.
On your serger foot there should be a couple of lines, these show you where your needles hit the fabric., If you are serging with 4 threads, the line to the left is your seam line guide. This is where your want to guide your seam line marks. The line on the right is the right needle position, don't really need to deal with it when serging with two needles/4 threads.
If you have a 3-thread serger, it essentially is for seam finishing as the seam created is not as sturdy as the 4-thread seam. If this is the case, seam your garment on your sewing machine, then trim your seam to the desired width on the serger.
If you pin your item together, place your pins parallel to the seam line and far enough to the left of the seam that the foot does not run over them. DO NOT serge over pins...you will end up replacing the cutter blade.
Practice, practice, practice. Sergers can be a little daunting, but once you know how to use one, you will love, love, love it.