What are your good tips/strategies for making a good character build in Oblivion?
The Elder Scrolls Wiki has a lengthy article on this very topic: http://www.uesp.net/wiki/Oblivion:Character_Creation
Perhaps the biggest: Plan from the beginning as to what kind of character you want to play. If you want to play a brawling fighter-type, eschewing magicka entirely, the Atronach might be a better sign than if you were making a mage. (Or inversely, a Dunmer[Dark Elf] with the sign of the Lord (I think it's the lord) won't suffer increased fire damage because of their innate racial resistance to it.)
If you are not modding the enhancement system, my strongest advice would be custom classes! Look at the defaults -- they're pretty decent, but often they use certain skills to level that you may not want/need with the type of character you're playing. Conversely, if you're looking for more of a challenge, you can put skills like athletics and acrobatics (both of which, I found, were hard to do simultaneously) in your custom class.
Remember that your skill choices will correlate directly to your attribute growth as well. For example, heavy use of blade will increase your strength. If you choose your class skills wisely, you can max out your character's most important attributes (whatever they happen to be to you) relatively quickly.
One important thing to note: There are no rules governing who may join the various guilds and factions. Thus, you can be a 98-pound-weakling with an arsenal of heavy destruction magicka and still be in the fighter's guild; conversely, you can be an all-brawn-no-brains axe-wielding thug and still become the archmage of the mage's guild.
One of the awesome things about Oblivion is that it is nearly infinitely replayable, simply on account of the extremely flexible class system. I've played through it completely at least three times (I lost track) -- once as a sneaky archer type with some magic for backup, once as a pure magick-using mage, and this most recent time as a close-combat sword-wielding maniac. (That was fun. I don't remember what I called that class, but the hardest part of leveling at higher levels was that I'd chosen both acrobatics and athletics.) Experiment and have fun.
Oh, finally, one last thing to note: Oblivion tends to level up the enemies as you level up. Thus, having more powerful weaponry at lower levels can make the game much easier than just constantly being on the level-up track. That said, by level 20 or so, just about everything is relatively easy. By level 30, the only issue you should have is exactly how to carry all your loot out of an Oblivion gate.
(My highest-level character was the most recent, the sword-wielding acrobatic guy, at 45 upon completion of all the add-ons.)
The interesting thing about this game is how you level up. Since you need to increase ten levels in your 'core' abilities in order to gain a level you can either try to make it really easy to level up by creating a custom class that has core abilities that you use all the time, or go the exact opposite and have your core skills the ones you use least often.
I'm a sneaky guy. I sneak everywhere, so having sneak would be good to level up fast, while athletics would help me level more slowly because you can't gain experience in athletics and sneak at the same time (in theory, anyway). The same kind of ying/yang can be found in the type of weapon you use and to an extent the type of armour you wear (although this can be mixed)
Selecting a character type should be dependant on the stat bonuses, not resistances. A breton with high magic can still be a fighter, but an orc or redguard may have more trouble casting higher spells later. Immunity/resistance to fire/poison/disease and even waterbreathing can be gained with items so they shouldn't weigh too heavily in your choice.
Ultimately though this game has tons of replay, and part of that is trying out new combinations. Go nuts and have fun!
After playing hundreds of hours of Oblivion, I finally made a pure mage class.
The clue is that if you want to be both able to cast powerful spells and at the same time wield the best weapons in game, it is easier to train a mage to use sword or the like rather than teach a pure
STR class to use magic, because (here comes the most important part) : you cannot use the mightiest spells since you don't have the mana for it.
That is a bit of a shame, since there are so many fantastic spells in the game!
Also, the question of whether you want to mod the advancement system or not is really relevant. If you do not, you might want to make sure you have a skill tied to each primary attribute. That way you can get to a better overall statistical level with a little extra effort. I don't think that is at all necessary, but if you like to min/max it is something to consider.