Hunter's Machete + 5 Health potions
This is the standard start on almost every jungler for season 3. Not only is it increasing your clear time by a significant amount, but this increase in clear speed means that you take much less damage from camps. Without machete you will clear slower and thus take more damage, making it very difficult for you to influence the game early, or even just clear the jungle normally for that matter.
Early "Core" Items
Investing in primarily "jungle-only" stats really hurts the income of a jungler, but upgrading machete to spirit stone is a necessary evil. Without any built in tankiness Sejuani needs some extra help in the jungle, which is exactly what spirit stone does. Not only is it giving some very helpful regen (similar to the Philosopher's Stone of season 2), but this increases your clear time even more over machete. In turn you will be taking less damage, spending less mana, and having more time to gank.
Ionian Boots of Lucidity
I cannot fault anybody who decides to purchase
; however, it is my opinion that Sejuani can influence the game most with CDR. It means that she can work toward having her W always up, her ultimate always ready to engage, get an extra slow off in a fight, and have Q up to escape sticky situations or catch people. As Sejuani you will be trying to gain objectives for your team during mid game, for which the extra CDR is most beneficial. All of your other items will contribute to your tankiness, so you can afford to build boots which don't contribute to it.
The reason to buy this item is basically the same as the boots: for the CDR. It has a nice benefit of some extra HP though. It has some great upgrades into team items, although you'll probably just hold onto the gem while you finish other items first.
Aegis of the Legion
This item is a godsend for tanks. It has an incredibly useful aura, but more importantly is the only defensive item to provide all three defensive stats (health, armor, magic resist). Definitely get this item almost every game, as it will help your and your team's effectiveness a lot. Make sure to tell your support though so that you don't double up on buying this item.
This item should also be purchased a majority of games, unless the enemy has almost no magic damage. Otherwise you're getting a ton of stats for the upgrade cost and making the aura even better for your team.
This item, at first, seems like a strange item to buy on Sejuani. The health and CDR are great, butr you're paying a lot for a damage and lifesteal aura, stats that aren't really very strong on Sejuani; however, this item isn't primarily for her. Sejuani excels best by helping her team instead of focusing on being a carry herself. Generally this is a late-game upgrade, although pick this item up earlier if some of your team is failing and it looks like a strong AD carry is your only route to victory.
Locket of the Iron Solari
Locket is going to be your other choice for upgrading your Kindlegem. This is great if your team is doing pretty well, but needs a bit more extra protection for teamfights. In particular this is better if you have a strong caster who is dealing the most damage in fights and needs a little extra oomph to get another rotation of abilities off.
A strong defensive option to also increase your damage output. If you get ahead grab this item early to increase your damage output. Otherwise you probably want Aegis (and sometimes Bulwark) finished before you put this together.
Randuin's is truly a strong item, and fills a similar role as Sunfire Cape. However, this option is more for when you and/or your team is behind and need some extra help shutting down strong enemy AD carries or need to protect your AD from bruisers. The active goes a long way toward these goals, and the passive can certainly helps reduce the enemy's power even more.
None of the enchantments are worth buying for Sejuani, at least until you're basically maxed out on items. You spend too much gold for effects that don't really help your role of being a tank or securing objectives. That said, if you want to pick one up later, Captain is going to be best for you, since they help our your team follow up on your initiations.
Sejuani has nothing that scales with AD, and her three AOE abilities let her clear very effectively with the percent damage increase of Spirit Stone. Pass on this item.
While flask has its uses, I just don't feel like Sejuani needs it. You clear fast enough to take little damage after the first two clears and your mana usage should be fine with your base regen and spirit stone.
Frozen Heart is great, but not for Sejuani. While extra mana is not bad, you don't need it like other champions do, which makes the mana an almost wasted stat. The CDR great, but it's better to get your CDR from other sources and then spend your extra money to invest in health. The real problem is that without any health, all the armor this provides is significantly less useful.
Any AP Items
Sejuani has a 2.6:1 ratio for ability power on a full rotation of her abilities, assuming you get maximum W damage. So you can't really burst anybody down in one rotation and her cooldowns are too high for AP to add sustained damage. Sejuani's real damage comes from staying alive in a group of enemies with her W active (which can easily get over 150 damage per second in late game). So, by building tanky you can be a strong frontline for your team while staying alive to get that consistent damage. If you invest in AP you'll be squishy and still unable to burst anybody down.
This item just does nothing. It's only HP, but no special bells and whistles. You're better off with Sunfire Cape or Randuin's in basically every situation.
Philosopher's Stone and Kage's Lucky Pick
As mentioned before, Sejuani doesn't scale well with AP, so Kage's isn't doing much for you, nor will it build into much useful for you. Philosopher's stone used to be much better, but Spirit Stone has mostly replaced it so the extra regen is just not needed.