Most likely you're teching wrong. It's possible to enter info era at t260 without any RAs and almost any start if you choose which techs to beeline and how. Try to reach these techs by these turns:
1. Education by t110
2. Scientific theory by t175
3. Plastics by t220
Normally you'd need to shave about 10 turns off these times to compete on deity, but we're talking emperor/immortal here, so you can be a bit lax. If you want to go domination VC, there are some guidelines you should follow.
Here are a few more science-specific tips:
1. You should have 3-6 core cities set up by t100. Also, NC is recommended t90 or earlier.
2. In core cities, population should be 10 by education, 15 by sci theory, and 20 by plastics.
3. If it takes more than 10 turns to build a science building and you have a decent/strong economy, buy those buildings. Otherwise save cash for unit upgrades - they're more expensive than you think.
4. Try to build PT and LToP; get great scientists for both. Scientists attained earlier than this should be planted; these scientists should be saved for bulbing.
5. Enter modern era by building Oxford and getting replaceable parts as free tech.
6. Bulb one GS for radio, another for plastics.
8. Get artillery; shouldn't be too long with labs and factories.
9. Enjoy as your technologically superior units crush rifles and muskets of other civs. Build frigates and upgrade to battleships; 4 should be enough.
7. Later, use rationalism finisher for rocketry and satellites.
8. Should any other runaways remain, use 2 GS from Hubble to get mech inf/nuke subs, tech/build nukes, and mobile SAM spam their air force to death.
9. tl;dr: get science techs and build/buy science buildings ASAP. I know cannons/rifles might seem enticing, but waiting ~20-30 turns for units that are more than twice as strong is more than worth it. Also, grow grow grow!
What units you should build, and when:
1. Early in the game: 4-6 ranged units and upgrade as necessary.
2. A pike, as they are stronger and more resistant to ranged attacks than swords.
3. Mid-game (medieval-renaissance): 4-6 melee units and 4-6 siege, to upgrade to artillery/infantry later. Caravel for exploration.
4. Later: naval units, bombers, mobile SAM spam, etc.
A word about defense:
In G+K, everyone is your enemy, but that doesn't mean you have to spam units to stay afloat. Learn to bribe enemies to attack each other, pick on weak civs to get work-together diplo bonuses, and to attack/defend with 4-6 ranged/1 melee unit. See Madjinn's videos for advice on early-game DOWs.
That's all the advice I can give. Hope this helps!