If you are doing well mid game or are approaching late game don't have enough for a HoT, a sange and possible heavens halberd for the evasion and just helping your team overall to lock down that annoying carry. Its a cheap way for more strength. Hot is for people with decent amounts of gold either late game or mid game. Its everything pudge could ever want.
It is important to grab a scepter on pudge, as it will make all the strength you've stolen even more useful, not to mention it makes dismember heal you. The armlet is one of your best friends. Make sure to have it toggled the instant you landed your hook, or even before you throw the hook as it has a 0.7 second duration before you gain the bonus 25 strength. This is equivalent to 10 stacks of flesh heap, people may look at you funny for buying it, but thats because they are noobs, so don't worry. If you have forgot to toggle after landing the hook and started dismember, don't worry you can toggle it during the channelled duration and not break the channel. It is extremely useful to deny yourself with, as you can start to rot when its toggled, and as soon as your current hp is relying on it where you normally would be dead untoggle it while rotting. Its almost always a suicide unless they had mad nukes. you can grab this even before scepter if you need it for the denying purpose. The treads will also add another 8 strength points to your ultimate. And speed is not of concern if you have a blink dagger and play it right. Also the hp regen is enough so you can spam rot, so the hood of defiance becomes less necessary, especially as it gives you no strength stats.
No explanation required for the boots of speed. I rarely upgrade my branches to wand and usually sell them over the period of the game, however it really depends on what your playing against. If they have alot of spam moves like bb, zeus, etc. then by all means get it. The urn is optional. Now this is extremely important so please read the next lines. Up until they nerfed the force staffs potential of increasing the hooks range, it has always been said the force staff is the way to go. I disagree. The blink dagger although doesn't provide you with any stats, requires no mana to cast, does not destroy trees, provides further distance, has a lower cd, and costs a little less. It really depends on who you are playing up against and how good you are at avoiding unnecessary damage. If you are up against tree haters like timbersaw, np, or any one who can destroy trees its probably a good idea to get a fs. If you do get a blink dagger, try blinking into a bunch of trees that are otherwise impossible to get into, and hook them into there. WARNING the use of rot is still considered you taking damage so the blink will have 3 seconds before you can you it. Try to make sure you land the hook before using rot. Also if you are better than average pudge try hooking the enemies team carry into trees and blinking out, so you can deal with the rest of the enemy first and leave him chilling there for later.
You can also purchase three branches on top of that and a second gauntlet, but it will take longer for you to get the bottle. However if you are feeling harassed or are just not confident enough to secure your kill with only one hook its a good idea to get one or two gauntlets and three branches. The gauntlets will also make it easier to last hit and can be made into an urn.
The recommended starting items, has three branches to allow you to pull of a second hook at lvl 3. So hook, rot, hook, success.