Missions & Complexes

Exploration sites are quite like missions. You need to fit appropriate tank for the rats and use effective ammunition. The only real difference is that you need to scan those sites.
Tengu is overrated so don't hurry to hop into one ( it is good of course but there are other good ships to do exploration in ).

Hisec
- Loki is the best
Lowsec
- Loki will work but it is not that good ( works great for scanning/support alt )
- Sliepnir is great
- Machariel - I don't fly one yet but my friend does and he says it is a real beast with scout/scanner alt.
- Panther - He also used this ships and was rather impressed with its effectiveness ( with scout/scanner alt ).
- Normal battleships are not intended for solo work but you can use them when in gang.

EDIT
Ships selection depends on region you are gong to do exploration in. As Minmatar you will be using mostly explosive ammo and that means you will do much better in Angel space. You can use t1 ammo with different damage types but then you cant use Barrage ( quite a big deal when using autocannons ).

For starting out exploring, I would suggest the Loki or Wolf and hopping over to Sansha space (not really that far from Min space TBH). Loki is a beast that can handle all the sites there easily and the Wolf has an epic Sansha tank and I've run all but the Vigil in it (I'm just wary of those webs in the Vigil). I've also used the Loki to run all the Angel sites I've taken it into, though the fact that I know how to blitz them by now probably helps with that.

Here's the Sansha Wolf fit I used:
[Wolf, Sansha Exploring]
Damage Control II
Centii C-Type Small Armor Repairer
Centii A-Type Thermic Plating
Capacitor Power Relay II
Gyrostabilizer II

1MN Afterburner II
Codebreaker I

200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
Core Probe Launcher II, Sisters Core Scanner Probe I

Small Capacitor Control Circuit I
Small Capacitor Control Circuit I

189 DPS tank, 33m sig, 217 DPS with RF EMP at all 5s

Here's the Loki fit I used for Sansha:
[Loki, Highsec Shields]
Damage Control II
Tracking Enhancer II
Gyrostabilizer II
Gyrostabilizer II

Stasis Webifier II
EM Ward Field II
Thermic Dissipation Field II
Medium Shield Booster II
Codebreaker I
10MN Afterburner II

Expanded Probe Launcher I, Sisters Core Scanner Probe I
425mm AutoCannon II, Republic Fleet EMP M
425mm AutoCannon II, Republic Fleet EMP M
425mm AutoCannon II, Republic Fleet EMP M
425mm AutoCannon II, Republic Fleet EMP M
425mm AutoCannon II, Republic Fleet EMP M

Medium Projectile Collision Accelerator I
Medium Core Defense Field Extender I
Medium Capacitor Control Circuit I

Loki Defensive - Adaptive Shielding
Loki Electronics - Emergent Locus Analyzer
Loki Engineering - Capacitor Regeneration Matrix
Loki Offensive - Projectile Scoping Array
Loki Propulsion - Fuel Catalyst

Hobgoblin II x5

420 DPS tank (535 if you carry a SBA and swap it out for the web/codebreaker, but I didn't do that outside of the Watch/Vigil escalation), 563 DPS with RF EMP at all 5s
For Angels I swap the hardeners and web for 2x Invul 1x Exp and it goes to 362 DPS tank (461 with a SBA for the codebreaker)

For an AF in Angel space, I always used my Ishkur, which performed beautifully. But for you, wanting to stick with Min ships, a Jag would probably be better. I was never really able to find a fit that really caught my fancy, but this one was about as good as I managed to figure out (Arty might be a bit better so you can kite more, but it seems to need a small CPU implant to fit even the smaller ones).
[Jaguar, Exploring]
Damage Control II
Gyrostabilizer II
Beta Reactor Control: Diagnostic System I
Beta Reactor Control: Diagnostic System I

Gistii B-Type 1MN Afterburner
Gistii B-Type Small Shield Booster
Gistum C-Type Explosive Deflection Amplifier
Codebreaker I

Core Probe Launcher II, Sisters Core Scanner Probe I
200mm AutoCannon II, Republic Fleet Fusion S
200mm AutoCannon II, Republic Fleet Fusion S
200mm AutoCannon II, Republic Fleet Fusion S

Small Projectile Collision Accelerator I
Small Core Defense Field Extender I

107 DPS tank, 36m sig, 175 DPS with RF Fusion with all 5s.

Hopefully those fits give you atleast a bit of an idea about getting into exploration. Personally, I would recommend tossing together that Wolf fit I listed (probably 50-70M all told) and fly over to Sansha space and explore around a bit. It's massively over-tanked for almost all their sites and should handle itself nicely for low initial investment.

I used pvp navy Domi ( with cloaky Proteus sitting on gate ) for some time and no one ever bothered to go in and catch me