Okay you've closed in on your target ship. You've taught it to mostly stay still. You've gotten your people across to it through various means, not all of them pretty. What can you expect and what should you bring?
You're probably wearing vacc suits or rarely combat armor/battledress. Vacc suits are pretty much equivalent to cloth armor. Most combat is at short or medium range which is ideal. An automatic rifle is all you need to send most intruders on their way. Better to blast them at the airlock before they get near easily damaged stuff. Auto rifles work equally well for attackers. Both sides will probably have electronic sights, not for accuracy so much as dealing with the lights going out. Make sure the sights can be used with a vacc suit helmet.
Snub pistols loaded with tranq rounds are a viable option. A tranq round will penetrate a vacc suit, especially at short range. A tranq round is unlikely to put a jump drive or power plant to sleep. As a bonus many vacc suits have a self seal feature that will let the person shot live without having to slap a patch on their suit.
Bring some flashlights. Use them after the fight or let the bot hold them because people shoot at lights in the dark.
Bring melee weapons. No really. Auto rifles suck at short range or closer and you might not want to shoot the engineer standing in front of the jump drive or the guy hiding behind the crate with those red warning labels all over it you can't read. A cut in a vacc suit turns an enemy into a guy scrambling for a patch. The fight leaves those guys fast.
Both sides need vacc suits. Unless the defending captain is a moron he's depressurized the ship. You don't want your crew or passengers sucked out into space if the boarders blow a hole in your hull to enter. Passengers are probably in a secure area in vacc suits or survival bubbles.
Some boarders (high tech pirates, Marines, cat-girls if you're lucky) will bring along cutting torches to remove interior partitions quickly and not be confined to corridors ending in a bunch of automatic rifles. This is not such a great idea. Fire sensors will tell the defenders what you are doing allowing them to prepare a nasty surprise for you on the otvher side of the wall you're cutting. Thermite or explosive charges are quicker but are harder on the ship's resale value. Starting a fire on a ship you're boarding comes pretty close to marching into the mouth of Hell for me.
Do bring an electronics kit and mechanical tool set to help open doors. Bringing a laptop along to hack the ship's computer is a popular trope. That's the sort of thing reserved for a hi-jacking. Any computer you bring aboard probably doesn't have the processing power of a ship's computer unless you have several tech levels over it. Cyber operations are possible but will probably take a lot of time.
You can try going in through the airlocks. this is pretty predictable and even if you force the airlock or hack it there's going to be six kinds of warning lights on the bridge. Find several entry points and make the crew cover them all. The reason the storm troopers acted like idiots in the opening of Star Wars is Darth Vader was behind them in a hurry.
Turrets are often overlooked as entry points. Remove the turret and enter through the iris valve. Hopefully the ship is evacuated. If the ship has a boat deck or cargo hatch you're really in business. Force that or override it and you immediately have access to a large area to assemble and plan further mischief.
Then there's the brute force approach, blow a hole in the hull with ship lasers. Blow a couple of holes and watch the defenders play guessing games. Even so it is likely you are going to come under fire almost immediately.
A shield is a good idea. Get the biggest robot with the best armor you can to stand behind. Flash grenades work great for an entrance too (you need air for a flash-bang grenade.) You could also just hold pieces of hull metal in front of your group. If you can't do any of this find cover quickly. This is why Marines use battledress. Even that is not perfect protection at such short ranges.
The crew will do their best to make their ship an inhospitable place for you. They may cut lights in their areas giving them concealment while high lighting you. They may shut off the gravity in your part of the ship to take you off balance. They will close iris valves and hatches on you. Some ships have interior weapons mounted. If they have enough time they may even rig booby traps. After all a space combat turn takes 1,000 seconds. That's plenty of time to string a tripwire.
The crew will probably depressurize their ship. Explosive decompression is no joke even in a space suit. You can get blown out a ship if the hole is big enough. You also wind up wasting air if you wait to depressurize until you get get a big hole. Though you might get lucky and have it sealed by a pile of crew.
A hole big enough to suck a man out would be big enough to cause a lot of other problems that might need tending first.
On entering the ship your first goal is to stay alive. If you made several false entries, used shock and awe and big metal robots to hide behind and have a good bunch of crew you made it at least this far. If you're in a hold or bay you have room to marshall your forces. Whatever you're doing, do it fast.
Why? Because at least some of the crew is trying to un-disable it. If they get the maneuver drive running you can kiss reinforcements good bye. If they get the jump drive going you're really screwed. If they get a turret online they can start shooting at your ride, which might start shooting back. That could make holes big enough to suck you right out by the way.
Lasers and missiles have no friends.
Forget the bridge. Go for the engineering deck. Even if you take the bridge someone in engineering may still retain some kind of control and cause headaches for you. The bridge probably has one access and is well defended. The drive deck often has several access points for repair and such and is probably easier to get into. Get in and shut down everything. Those jittery types on the bridge might cause overloads or systems failures to damage your ship.
If life support is not controlled from the drive deck that's another option. If you can vent all the oxygen in the ship the crew is stuck in spacesuits with a day or two of air and much more inclined to be reasonable. If help is on the way this isn't such a big deal.
Hulls will affect your tactics. Needle or wedge shaped hulls will limit flanking actions. Dispersed or close structures may afford the most points of entry but then each section can be sealed off more easily. Spheres and flattened spheres are perhaps the worst to defend. They have a small surface areas and high volume with plenty of decks for their tonnage. Once they get breached attackers can spread out quickly.
Hopefully I've given some ideas for you to use to make your next boarding operation fun for you and a living hell for the characters.