Preface: I will guide you through this under the assumption you have empty halls. My goal is to get the most done for you without "grinding." If your goal is 30 points, do not hassle yourself with a PvP statue.
Section 1: 10/50
Play through Factions with a [Ritualist] and get the [black moa], [black widow], and the [imperial phoenix] along the way. You should use a bar similar to [this].
Once you have beaten Factions and acquired these pets, beat EotN. In the [Central Transfer Chamber], there is a [challenge mission] to do. Beat it to obtain a [Cloth of the Brotherhood] and put it on one of your heroes.
Progress Note: Now you will have 5 statues under your [Fellowship Monument], and you will have 5 of 8 possible points. You will have Hero of Cantha and Protector of Cantha in your [Honor Monument] from doing Factions along the way. Your HoM will be at 10/50. A complete beginner who stays on task can expect section 1 to take 25 hours. Someone enlisting the help of a veteran player can expect 15 hours.
Section 2: 14/50
Now it is time to beat the other two campaigns, Prophecies and Nightfall. Doing so will contribute 4 more statues to your Honor monument. You will now have 6 statues in the display, which is enough for 3 more points.
Now that you have beat the games, you should be relatively comfortable with how to do things. As such, it's time to challenge yourself. Beat them all (except EotN) in [Hard Mode] now. This will have gotten you 4 more statues for your HoM, bringing your total up to 10 and earning you another point.
Progress note: Now, you will have beaten the games. Congratulations. You're well on your way to getting a satisfactory HoM. Having beaten these, you should have at least 150k left over from loot you've collected and sold. It's time to put that money to use. Someone who was a beginner at the beginning of this guide can expect section 2 to take 75 hours. Someone enlisting the help of a veteran player can expect 50 hours.
Section 3: 19/50
Head to [Kamadan]. Buy a [Black Moa Chick]. One can be had for under 60k.
Pick either a mini [Lich]/[Rurik]/[Pig]/[Celestial Rabbit], and buy it. One can be had for under 40k.
Now, buy the 18 cheapest minis you can find.
Fungal Wallow, Hydra, Jade Armor, Jungle Troll, Necrid Horseman, Siege Turtle, Temple Guardian, and Whiptail Devourer are all 1st year common minis and can be had for <2k each.
Aatxe, Fire Imp, Heket Warrior, Juggernaut, Mandragor Imp, Harpy Ranger, Thorn Wolf, and Wind Rider are all 2nd year common minis and can be had for <5k each.
Abyssal, Cave Spider, Cloudtouched Simian, Forest Minotaur, Irukandji, Mursaat, Raptor, and Roaring Ether are all 3rd year common minis and can be had for <10k each.
Progress note: You will now have 5 points in your [Devotion] monument, bringing your total points to 19. Time taken will depend on market availability. Purchases done during peak market times can be made in under an hour.
Section 4: Accumulate Money
Now, you need money. "What's a good way to earn money?" you may ask. [DoA] is a good way to earn money. It's time to put that ritualist to use. [Frostway] is a team composition designed to get through DoA in <1:30 in Hard Mode. One run will net you over 50k, and the 1st one will even put another statue in your Honor monument. Do 13 runs. That's <20 hours invested, and you should now have over 650k.
Section 5: Buy all the things!
1. You will need to buy 1 oppressor weapon, 3 destroyer weapon, and 1 torment weapon. You should be able to obtain all 5 for around 320k. These will bring your [Valor] monument up to 5, bringing your total points to 24, and leaving you with over 300k to buy more things.
Buy 5 more Cloths of the Brotherhood for 5-6k each and put them on heroes. Now, you still have almost 300k, and 25 points in your HoM.
Time to buy some armor. Remember, you do not need the head piece to put an armor set in your HoM. You can buy [Elite Luxon] armor for <110k. Jade sells for less than amber, usually, so this is your best option. Craft yourself a set of [Ancient armor] for <50k. Craft yourself a set of [Norn Armor*] for 50k.
*20k of the 26k points you need in your Norn title are obtained by turning in the [Hero's Handbook] you completed when you did EotN. 3k of the points came from completing 3 of those quests. The remaining 3k should have been completed with bounties during your ventures.
Progress note: Now, you will have about 100k left and 28/50 in your HoM. Buying the rest of this stuff will take less than an hour in an active market.
Section 6: 30/50
Now, fill up the rest of your Fellowship monument. You can buy most armor pieces for ~5k. You need 20. You have 100k. It's almost like magic. Congratulations! You just got 30/50 in your HoM in under a week of playtime with no prior experience!