Well if you really cannot stay away from horses by your own will there isn't any advice that will help that much I guess. Since the game is called mount and blade I would say horses are meant to be part of a character's gaming. I personally can stay away from horses but that is only a personal choice since it depends on the character I play (I have a few of them).
I would imagine what you cannot stand is the reduced mobility, the fact that when you play as infantry cavalry can be a real pain in the ass since they charge you to the ground or you cannot catch them.
If I were you I would take it this way:
Do not reduce your mobility too much since the speed of your character will depend a lot on what you have equipped. Therefore wear lighter armor (not exceeding 20 in weight), the sarranid guard armor is in my opinion perfect for the task, or the one their cavalry and infantry uses especially when they are "lordly" items.
To prevent cavalry from charging you to the ground all the time you can stop them with a lance, a spear, or pretty much any weapon of this kind (just stab them when they charge you it stop them right away).
Then bring a huge shield with you, resistant, decent speed rating, and a lot of hp. In my infantry characters here it would be a huscarl's shield.
A one handed weapon such as a heavy war axe is also very good in this condition. It might be called heavy, it might not have the best stats but I haven't found a better match for infantry gaming. It is faster and more effective than the stats allow to think.
Then simply wear mail mittens and boots (simple mail boots or sarranid ones). Sarranid veiled helmets are also good here.
On top of the weapons you already have I would recommend jarids or javelins, a large bag. It is very convenient when a mounted unit is still close enough to throw one in his face and is trying to run away.
Unfortunately to be a versatile infantry unit managing skills when you level up is not the easiest task, you need to balance str, agi, int and char in a way that allows you to be good in the field and as a leader for your company. Agility is here very important with athletics. It will increase your attacking speed, the reactivity of your character and your running speed.
I would overall say that playing as an infantry lord is a lot more of a challenge at the start. For example if you do not have men to back you up yet but you get attacked by a bunch of bandits they will overwhelm you.
Therefore you should stay as a cavalry warrior until you get enough strong soldiers with you to be safe against any attacks.
That's where it gets tricky: remember you had to balance every skill wisely, which means you cannot emphasize charisma and leadership too much and that won't allow you to have a lot of soldiers around. Which is why you must maximize the soldier capacity in your party with your renown, win tournaments, it helps a lot and gives you a decent amount of money with the bets on yourself.
Now that you can have around 70 soldiers with your make sure they are good hardened bastards that are difficult to take down, chose rhodok sergeants and veteran spearmen. Bring along vaegir archers and marksmen. In the field always put your infantry in fornt of the archers. Sergeants can take a beating so no worries about them (I would suggest to not neglect surgery skill here, it really helps a lot in raising a powerful army).
Do not start with a high difficulty, start slowly with the lowest one to get used to fighting as infantry and raise it little by little.
As for the kingdom you should join I would stay away as far as possible from the rhodoks. Except for their sergeants and sharpshooters they only have weak and powerless soldiers. Join the Nords, they are very good melee fighters and even though they lack skills in skirmishing as an overall review, they make up for it with a strong infantry starting from nord trained footmen.
There probably are some other advice I could give you but I cannot think of any right now.
Enjoy your gaming !
EDIT:
do not be impatient this takes time and a certain amount of fighting and scavenging money (take prisoners and sell them, loot bandits when you fight them and sell the items you get when travelling in between cities where tournaments are for money)
AND ABOVE ALL: do not be afraid if you get knocked out by bandits and taken prisoner and everything, you won't lose that much, and if you can catch them and beat the rest of them you can have most of what you lost back and if they have your soldiers as prisoners or other prisoners you are almost fully back on your feet !
