Do you want a dude who throws lightning bolts and stabs people? That doesn't work well in SR and is why (well, one of a number of reasons why) the sample character Combat Mage is bad.
I'll have to disagree on this point. Slinging spells and using blades can work VERY well, depending on the way you go about it. But Umaro is right, first you must come to terms with what you are, and what you are not. You ARE a mage who can hold his own in melee combat. You are NOT a tank, unless you are using a possession tradition, and have a high Force spirit riding you. Never, ever believe that you can soak more than the troll street samurai.
I have a custom tradition I made for a Swordmage, and you can find it
here. However, most of what makes a follower of that tradition a swordmage is the fluff. You can easily take a Hermetic, Shaman, Voodoo priest, or whatever other tradition you like, and make them a mage who wields a sword, and be just as effective, mechanically.
If you are using a possession tradition, spirits with Elemental Aura are your bestest friends. +4 DV to your melee attacks, anyone who attacks you in melee takes the spirit's Force in damage, and either way those get a -half AP. With this setup, you want to have a solid Summoning pool (10 dice or so is fine), and don't spend karma on anything you don't ABSOLUTELY have to until you initiate and take Channeling.
If you aren't using a possession tradition, get a Sustaining Focus set to Health spells (I'd do it at Force 3), and have Increase Reflexes sustained on yourself 24/7. This will make you glow in the astral, but if you aren't an initiate with the Masking metamagic, then you'll show up on astral scans anyways, so the point is moot. Your favorite spell, which you will either cast at the very beginning of combat or keep sustained if you can afford the -2 or the sustaining focus is Combat Sense. Adding your hits on the spellcasting test to all melee and ranged defense rolls is a beautiful thing. Your second favorite spell will be [Element] Aura. Similar to the spirit power, this makes melee go from 'meh' to 'did he just cut through a plascrete wall in a single blow?'
In either setup, I would put Blades and Spellcasting at 5 immediately out of chargen, with specializations if you like. Grab Pistols or Longarms if a shotgun is your thing, and Dodge while you're at it. I wouldn't get more than 3 in either one, especially if you're a possession mage. Don't bother with Automatics. They eat ammo like mad, especially for something that isn't your primary focus. If dealing in pistols, get two guns (smartlinked) with just enough RC to keep you from suffering penalties. Put ExEx in one, and SnS in the other. If you're running low on nuyen, skip the ExEx one. Counterspelling and Summoning are definite gets. Binding is nice, if you have the BP. Don't bother with Banishing. A weapon focus does the job much better, especially with the aforementioned -half AP from elemental effects. Grab a single target mana combat spell and physical combat spell. Manabolt and some elemental spell (Flamethrower, Lightning Bolt, etc.). Make these your primary ranged attack. Get fetishes to help with drain on these, if nothing else, but don't overcast as a rule, unless your DM is one of the idiots who uses that optional rule for gimping mana combat spells. You're looking to get consistent damage without taking crippling drain, especially since you will have spells sustained. For other spells, grab one area distraction spell (Orgy or Darkness are my faves), and then pick the rest to fit your character. When things get close enough, a weapon focus plus that -half AP is going to be deadly against almost anyone. With all that, I'd be surprised if you can afford to get your Body above 3 or so. Personally, I wouldn't bother. Get yourself a Lined Coat, and SecureTech PPP armor or a Death Mask to bring you to 6/6 armor. Remember, you are not a tank, unless you have a Force 5+ spirit riding you. Your objective is not to be hit in the first place.
Another word on spells. These are the spells I consider to be absolutely critical to a combat mage in general, and a swordmage in particular. You might not be able to get all these at chargen, but this is something to work towards, as well as anything you find that would be useful to your playstyle. You don't need to have all of these, but it certainly won't hurt.
Manabolt/Stunbolt - Low drain ranged attack. For aesthetic reasons I prefer Manabolt for a swordmage, but YMMV. If you want, you can grab the area versions as well, but while they are great at ambushes and taking down groups from a distance, in practice they aren't much use in actual firefights when people are behind cover, or in close quarters, or your allies are in the radius, etc.
Flamethrower/Lightning Bolt - Or any [Element] version. There's a list of special damage types in SR4A and Street Magic. Any one will do nicely. Again, the area versions are nice, and actually more useful than the mana spells, since they can hit things you can't see, and can prove very good at, say, clearing out a fortified position. But the high drain makes it something you can't cast repeatedly, which means you ought to consider other options, like getting the sammy to send a grenade that way.
Heal - For the love of all that is holy, take this spell. A dose of healing in the middle of combat can turn the tide from "we're all fragged" to "how the hell did we get out of that one".
Combat Sense - Your main focus is in not getting hit. This spell makes you harder to hit. Do I need to go on?
Deflection - See above. However, you only need one or the other. Penalties for sustaining both will hurt, and getting tons of dice to avoid all attacks tends to make your DM pissy.
Increase Reflexes - Always have this on yourself, sustained through a focus.
Darkness/Orgy/Mist - Area debuffs are your friend. Everyone in the area has a penalty on shooting you? I call that a win.
Trid Phantasm/Trid Entertainment - Excellent battlefield control spells for distracting an enemy. Because if a dragon pops up in the middle of a firefight, chances are the corpsec aren't going to be shooting at you for at least a few seconds.
[Element] Wall/Physical Barrier - More battlefield control. While they might not be as effective as their D&D counterparts, they do a great job of keeping people from shooting at you for a bit.
Ice Sheet - Everyone in the area makes a check or falls on their face. Vehicles make a check or crash. Battlefield control at its finest, with reasonable drain, and no sustaining.
Petrify/Turn to Goo/etc. - This is a personal preference thing, really, but if your DM uses composure checks, then seeing the commander turn into a statue mid-command tends to demoralize the troops. Plus, you can still question them later. Or, if your DM allows a permanent version of the spell, then you have a sideline as an 'artist'. Turn to Goo is also a very good way to collect an enemy's cyberware, whether they're through using them or not.
