What follows is a crash-course in which countries have which upgrades, and how they effect the various units of the Artillery Tank regiment. Also included is a generalized upgrade order, which should give new players an idea on what the different upgrades effect, and when to research them.
 

By no means do you have to get every upgrade possible, but at least try to keep pace, or stay ahead of the upgrades of your opponents. Make sure to pay attention to terrain, and scout the enemy, to help decide which upgrades best suit your current in-game situation (and the troops you have in the field).

It is important for newer players to understand which upgrades to get, and when to get them, to be successful in online play. Keep in mind if you ask 10 different people, you would probably get 10 different answers to this question, so what follows is a general guide which in no way is cast in stone.
 
Many of these upgrades will have already been researched at earlier stages of the game, but we will proceed as though you were going "straight arties". You will need both the Motor Pool and Artillery Brigade to research these upgrades, and if playing as Japan, you will need to keep them both to continue deploying Arties [why?]. With all the other countries you can produce arties with only an Artillery Brigade, so you are free to sell your Motor Pool after your researches are finished, and replace with a HQ to help your late game economy [see tent swapping]
 

Some upgrades effect all vehicles, such as Mechanical Reliability, but many of them only effect certain units. Before you order any performance enhancing upgrades you must first make sure these upgrades will actually effect the units you have in the field. For example, many of the upgrades that effect armor will not effect the Arty Tank Unit, such as Diesel Engines, Gyrostabilized Tank Guns, and Schurzen (they do effect the support vehicles of the Arty Tank regiment).
 

If you are going "straight arties" very important that the first thing you do in online play is to deploy a few recon ASAP, to capture as many nearby cities as you can, especially that city in front of your base! Don't worry about upgrades until you have captured and secured those cities! Also, make sure your teamates know you plan on going "straight arties" and be ready to alter your plan if your allies need help.

If the upgrade listed is not available to your country of choice, or does not fit your situation, simply skip to the next upgrade in the list.

When playing as Britian, Japan, or Russia, Military Surplus will generally be your first upgrade in ANY online game, regardless of whay type of build you plan on. Important to get your economy going in the early game! Most people research this upgrade somewhere after the 2nd to 4th HQ deployed.

Available to Germany and Russia, researching this technology helps to transform them into late-game powerhouses. The -10% Cost this upgrade offers esentially breaks down to "Buy 9, get the 10th free!", which makes a huge difference over the course of a long game. Make sure to research before you deploy your armor for maximum savings. Even more useful when used in combination the Rapid Deployment special op available to General Rokossovski

Britian, Russia, and the United States have the advantage of Mechanical Reliability which offers an additional 10% health. This can be a deciding factor in close battles, and since it effects all vehicles, will offer benefits for the remainder of the game

Available to Britian, Germany, and the United States, Improved Fire Control will improve the attack speed of all artillery based vehicle(s) by 25%. Any attack speed upgrades offer huge advantages in combat, and allow you to get more rounds down range in less time.

Every country except Germany has the option to upgrade their Arty Tanks with Long Range Artillery. We have to assume that if you are deploying Arty Tanks you plan to use them for what they are best at, Bombarding the enemy from a distance. This upgrade will increase that distance, allowing for more stand-off space from your opponent(s).

Available only to Germany, the Bonus +3 Morale offered by Advanced Armor Training will help keep all armor units from routing as easily, and helps especially vs the Arty Tank regiment. Just beware that the better a regiments morale, the more likely it will fight to the death.. So, as always, make sure to retreat units before they die.

All regiments will benefit from Foraging, allowing for quicker healing time while in zone of supply. Always get Foraging before Plentiful Ammunition as it costs less and gives a larger bonus. Only available to Japan and Britian, this upgrade is often used to upgrade British SaS or Japanese Commandos/Mortars during the infantry stage of the game. If you have yet to research this upgrade, get it now!!

Same deal as Foraging but costs a little more ($100 instead of $75) and offers a smaller bonus (only a +10% bonus instead of +15%)

Germany has no way to upgrade the health of their vehicles, but Schurzen offers a +15% AP Resist for armor units... a bonus that is not available to any other country. This upgrade would have come much higher, but it does not effect the Arty Tank Units of the Arty Tank regiment. However, it will upgrade the supporting vehicles of the regiment, the light tank unit; so it is still a worthwhile upgrade that helps during direct engagement. Since Germany has no Long Range Artillery, their Arty Tanks will be closer to the front anyway... Also, Schurzen does offer greater resistance to the Kamikaze special op, but has no effect on any of the other special op bombs

The "mack daddy" of all armor upgrades, Gyrostabilized Tank Guns offers a massive +10 attack value to all armor units (excluding the Arty Tank Unit). This upgrade would have come much higher, but since it does not effect the Arty Tank Units of the Arty Tank regiment; your money is probably better spent on the upgrades above, first. However, it will upgrade the supporting vehicles of the regiment, the light tank unit; so it is still a worthwhile upgrade that helps during direct engagement. A much more valuable upgrade when used for "all armor" regiments such as Heavy Tanks..

A regiment will only move as fast as it's slowest unit, in this case the Arty Tank Unit, which is uneffected by the Diesel Engines upgrade. Which means when the regiment is at full health, there will be no max speed bonus received (the speed is only increased if the "Long Toms" are dead or yet to form). The +15% Max Speed will help your regiments get to the front faster when first deployed, since the Arty Tank Units are the last to form after the regiment is first deployed. It can help with retreating if your "Long Toms" have been killed.

Available to every country except Russia, this upgrade effects just about every structure and unit in the game. Gives a Bonus of +5 Detection Range for units, and +5 Supply Range for structures that provide a zone of supply. Though the effect may seem small, it does make a difference when laying out supply lines, detecting enemy troop movements, and also helps any regiment that has the bombard ability. Alot of players consider this the last upgrade they get for their arties (late in game), but at only $50 you have a little freedom when you would like to research it.

Once you reach the armor stage of the game, techniques such as leapfrog entrenchment really start to make alot of sense, and if you like that technique, get this upgrade to speed up the advance 25% (if available).

Although AA defenses are seen less and less each day in online play, there are times when building AA bunkers makes sense. Moving your Corp HQ often will help protect against airborne attacks, but offers no protection against airpower. If you see airfields or bombers, it's time to start building AA; and if you are build AA bunkers, make sure to get this upgrade if it's available.

There is no magic upgrade order that will work in every situation, so be able to adapt your strategies and tactics to keep your gameplay fluid.

"The highest technique is to have no technique. My technique is a result of your technique; my movement is a result of your movement."
^{Bruce Lee}